Sage Reference Manual
Search.setIndex({envversion:42,terms:{four:0,extcode_dir:15,prefix:[1,41,24],sleep:[9,23],savea:17,rnorm:40,issquar:15,whose:[12,1,2,38,17,18,40,7,43,44],basic2:15,typeerror:[15,1,38,39,5,41,31,20,44],sorri:9,homepag:24,gap_funct:20,concret:43,matlab:[],under:[27,3,18,40,7,10,43,33,24],aux:28,libsingular_gb_standard_opt:41,spec:15,maximafunct:1,getverbos:15,digit:[34,27,1,17,41,21,39,24],everi:[15,25],recommended_b1:17,erzsebet:20,rise:0,quantif:0,touchup:38,drfile:27,interfacefunct:[2,11,43],sage_object:[2,17,4,6,10,22],qsieve_nonblock:34,jacob:41,affect:7,viewabl:40,genfiles_mpfr:27,interfaceel:[2,11,43],to_sag:25,wegner:20,"34m":17,cmd:[1,16,17,4,7,9,11,44,41],handout:0,factori:[33,21,44],vector:[25,0,15,3,40,41,19,32],matric:[],aachen:20,x86_64:9,qsiev:[34,17],use_disk_cach:[15,38,3,18,40,42,43,24],direct:3,commerci:[18,42],consequ:41,second:[34,43,32,0,26,15,37,23,3,18,27,36,28,19,20,10,11,44,24],"10y":17,even:[13,25,39,15,1,17,32,7,9,10,21,44,41],asin:[27,1],qsieve_block:34,neg:[18,1,2,44,24],introspect:2,singulargblogprettyprint:41,tarski:0,roundoff:43,intvec:41,"new":[0,1,2,3,7,9,11,13,32,15,16,18,19,20,21,24,25,5,33,38,39,40,41,42,43,44],symmetr:[1,38,44,43],my_matrix:[31,35],ever:15,elimin:[25,0],kaup:20,behavior:43,set_gap_memory_pool_s:9,never:20,here:[13,0,15,1,41,20,10,43,44],matlabel:35,j_1:0,spkg:[9,38,24],reduce_load_maximalib:44,"27y":17,quit_on_fail:[9,11],spec2:15,mccallum:0,p_1:[43,0],dummy_integr:44,ansgar:20,reduce_load_mapl:18,precis:[43,41,9,21,39,28],galoi:39,factoris:21,ako:20,tachyonrt:6,synchronis:11,"18x11y2":41,fourier:24,isomorph:21,schur:25,gap_el:20,prpye:17,unix:34,requirepackag:20,txx:27,ymin:[4,43],ord:21,unit:[21,43],highli:17,plot:[32,1,4,40,7,10,43,39],dna:22,describ:[12,13,43,0,27,2,4,6,20,11],giac_consol:24,commandnam:24,true_alexander_du:12,test_qf:0,datadir:39,newfn:7,overhead:[13,41],recommend:[1,21,17,9],preview:1,type:[0,1,2,3,31,6,7,9,10,13,15,18,19,20,35,22,24,25,5,21,38,39,40,41,33,43,44],until:[15,18,34,26],qepcad_consol:0,swap:[9,36],alberto:27,relat:[43,0,1,38,7,21,44],notic:[1,38,3,18,5,9,24],"__iter__":25,exce:11,gammainc:32,hold:[41,0],must:[0,2,7,9,10,13,32,15,17,18,19,20,21,24,25,27,30,33,34,37,40,41,42,43],join:[15,9,6,22,27],quartic:28,restor:[9,23,41],setup:19,flori:[1,2,11,44,43],axiomfunctionel:38,functionnam:3,erf:[43,32,44],"18x7y5":41,introduc:0,qvar:0,akin:20,hansen:[5,40,42,30,3],root:[36,0,15,17,3,10,24],exact0:0,pierr:[1,2,11,44,43],overrid:25,give:[34,0,2,3,18,7,44,28],tolrel:27,cascmd_loc:24,remote_machin:19,doublefloat:38,rngint:15,cartan:3,want:[34,0,17,3,18,40,7,20,9,24,45],umin:43,genfiles_mintid:27,david:[35,25,43,1,39,41,9,32,21,44],hagiya:33,kroneckercharact:15,end:[13,0,15,17,18,20,10,24],hoc:15,quot:[20,40,41,24,19],gapel:9,ssbasi:15,wcbrown:0,classifi:10,i686:20,how:[12,35,0,26,15,1,2,38,17,18,5,43,7,19,31,9,11,23,41],recoveri:39,env:6,scrambl:36,answer:[0,37,1,2,18,35,44],verifi:[15,5,33,38,0],"_singular_":41,wolfram:7,recogn:40,after:[21,0,15,23,18,8,20,11,24],yuasa:33,lab:40,diagram:3,befor:[34,0,23,17,4,41,9,22,44,24],wrong:18,beauti:23,lat:30,gfq_gap_to_sag:9,parallel:[],demonstr:[43,0],attempt:[20,2,7,41],third:[10,36,0,26],clear_prompt:11,maximaabstractelementfunct:[1,43,44],think:[15,16,14],like:[35,25,0,26,15,1,23,17,18,27,43,7,31,32,21,40,44,24,41],receiv:3,maintain:20,environ:[31,35],invlex:41,enter:[20,43,0],display2d:[1,44],order:[12,43,25,0,32,15,17,3,18,40,7,9,10,21,42,24,41],origin:[14,0,18,19,11,24],eval_pol:3,composit:17,partial_fraction_decomposit:43,offici:12,becaus:[0,15,1,38,40,41,19,31,20,35,24],"3x2y":25,keyboard:20,flexibl:41,unizar:27,fix:[25,26,15,1,32,27,41,30,9,43,44],better:[18,1,10],magma_fre:[15,37],sr_to_max:44,mself:15,persist:[],comprehens:40,taiichi:33,easier:14,variable_list:10,them:[38,3,18,10,33,24],anim:22,thei:[9,40,41,0,26],prefer:[18,24,0],database_gap:9,interfacefunctionel:[2,11,43],"break":[20,23,41],dickson:17,interrupt:[21,1,38,9,5,20,11],heiko:20,isen:11,scilab_consol:31,choic:[18,0],grammat:11,alex:[20,10],tmp_tides_delta:27,sing_283:41,unpickl:[15,1,41,9,43,44],mupadel:42,"1x1":41,timeout:[9,11,36],each:[13,40,25,0,26,15,2,17,3,27,41,30,8,9,10,21,43],debug:[40,41],expr_1:43,side:[22,41,0],mean:[0,18,40,41,20,24],slist3:7,b2scale:17,gctime:43,buchberg:14,resum:17,coerceabl:15,doug:7,format_cub:36,mobj2:7,extract:[],"24x":3,cubexsolv:36,uunizar:27,r_name:40,symmetricgroup:[9,2,20],content:10,adapt:24,plot3d:[4,1,43,22],output_file_cont:10,got:[2,11,23],"_sage_var_x":[1,44],linear:[31,1,38,32,43],get_series_precis:39,situat:[15,44],ntt:17,free:[],standard:[12,40,36,41,0],function_iter:27,nth:24,findroot:7,maximalibfunct:44,uiuc:25,fairli:0,traceback:[0,39,15,1,2,17,3,40,6,41,30,20,31,9,33,11,44,28],filter:15,fusionconjugacyclass:20,phcobject:10,"230m":17,isn:[9,38],sol_path:10,regress:40,subtl:[15,1],onto:[11,0],sageobject:[2,17,4,6,10,22],rand:[31,32],rang:[],derivedseri:20,nameleft:15,ellan:39,grade:[15,25],tachyon:[],independ:[32,24,19],rank:[15,41,28],hook:15,instruct:[7,24],alreadi:[9,2,7,24,41],hoon:0,wrapper:[],agre:[9,7],cartesian:25,pexpect:[],airi:32,top:[40,33,39],macaulay2el:25,revlex:14,sometim:[18,9,43,44,0],fiction:16,exponenti:[25,41],too:[43,44],tol:43,final_stat:0,john:[6,32],"17m":17,maxima_lib:[43,44],consol:[2,3,4,31,7,9,11,13,32,15,18,19,20,21,24,25,28,5,33,35,38,40,41,42,43,39],tool:[27,10],took:[34,17],ttolrel:27,mrat_to_sag:44,incur:13,somewhat:[18,21],signum:44,set_truth:0,eps_top:15,past:40,target:[1,43,44,9],keyword:[25,0,38,17,40,41,5,45],provid:[12,13,43,25,0,15,17,40,7,20,31,9,21,41],expr:[25,15,18,7,20,9,21,44,41],eq2:7,tree:[17,0],range1:4,project:[30,40,38,41,0],matter:0,singularfunctionel:41,monomial_id:12,exteriorpow:41,equationord:21,thu:[25,41],fashion:0,modmuln:17,rai:[],raw:[1,10,44],rat:44,seed:[32,15,1,2,17,40,41,31,9,39],manner:[32,15,1,41,9,21,39,7],increment:17,rfunction:40,dev_off:40,seen:0,seem:[1,42,21],ellipticcurv:15,sage_poli:41,reduce_load_giac:24,client:[2,11],findminimum:7,thoma:[20,14],simplifi:[18,24,0],is_fricasel:5,c_skew:10,though:[17,8],option_nam:41,object:[],broun:12,monomi:[],regular:10,current_r:41,letter:36,bsd:[5,38],typ:31,everyth:41,tradit:35,external_str:25,don:[0,26,15,7,9,21],simplif:[24,0,44],doc:[1,40,43,24,9],doe:[13,43,32,0,26,2,7,20,9,10,11,44,41],dummi:40,declar:41,maxima:[],section:[35,32,1,2,3,31,20,11],dot:[40,43,25],get_magma_attribut:15,"__str__":40,random:[34,35,25,0,26,15,1,2,17,20,32,18,41,19,31,9,42,21,39,24,43],sage:[],radiu:0,syntax:[],pkg:9,radic:20,qformula:0,mwrank:[],is_lispel:33,fileint:27,involv:[],absolut:[27,40,43],bourbaki:3,test_equ:10,configur:[17,24,0,39],get_gap_memory_pool_s:9,bust:20,"__call__":[6,25],axiom:[],niemey:20,reult:27,stop:[36,17,26],linux:[18,40,20,9,21,39],report:[15,43],reconstruct:[40,25],net:[5,1,43,44],quadraticsiev:34,gbyte:20,mmarco:27,sage_getsourcelin:41,max_workspace_s:[9,21],shape:0,gpfunctionel:39,"public":[27,43],reload:[15,41],bad:[10,43],qepcadrc:0,plot_multilist:43,unexpectedli:11,pfeiffer:20,commandlin:[9,6],roberto:27,mathwork:35,sageinspect:[15,41],pcore:20,sample_point_dict:0,mwrank_consol:28,num:21,result:[0,1,3,45,9,10,15,17,18,20,21,24,25,5,38,39,40,41,42,43,44,7],fail:[34,32,17,6,41,8,9,10,43,44],bess:32,numberconjugacyclass:20,best:[13,17],cofactor:17,quad_qag:2,said:0,tensor:25,easi:[13,0,20],sigint:9,yet:[18,17,41,0,30],test_fil:30,figur:[7,0],sage34:21,pts_list:43,variat:0,my_scalar:[31,35,32],mul:27,awai:40,mun:[18,24],gdiv:39,attribut:[15,20,2,41,19],sgi:6,accord:35,uppercase_q:[5,38],extend:[15,21,41,0,39],physicist:3,sophist:[31,24],assignnam:15,extens:[25,0,15,17,40,6,7,9,24,41],"141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068b0":1,toler:27,wstein:21,tmpfrts_pow_t_c:27,maxima_10:1,"123106i":40,tmpfr_init2:27,generate_docstring_dictionari:41,temporary_fil:27,howev:[25,0,1,3,40,7,8,9,43,44,41],against:[27,41],facet:[12,36],elliptic_curve_method:17,logic:0,uni:41,login:19,solve_linear:43,com:[12,21,7,45],"16m":17,foral:0,kwd:[2,3,7,9,11,15,17,19,21,22,23,28,41,25,26,31,42,37,40,24,33,44],conjug:42,bettina:20,reduce_load_octav:32,height:28,permut:14,"16x":3,path:[35,32,0,40,15,18,27,6,7,30,20,31,9,10,11,22,42,24,45],diff:[18,1,43,44,24],summat:44,assum:[12,20,24,0,44],tstatic:27,p_sy:10,union:0,p_2:43,ellglobalr:39,three:[25,0,26,15,41,19,9,42,21],been:[0,1,41,30,9,44],demo:[15,43],expectel:[21,25,32,15,1,38,39,3,18,35,7,19,31,9,42,11,40,33,24,41],beer:21,much:[12,14,0,26,1,23,38,40,41,5,9,21,44],is_singularel:41,advers:15,set_magma_attribut:15,expect_quital:8,pro:42,"__len__":25,quickli:[15,38,36,43],macaulay2:[],regul:28,"25m":17,suppress:41,maplesoft:18,xxx:2,gap3record:20,ani:[34,25,0,15,1,2,38,32,18,5,7,31,9,42,35,44,24,28],write_mp_solut:27,dave:17,lift:41,child:[2,11,23,19],"catch":44,spin:22,intfil:27,plot2d_parametr:43,ident:[20,2,41,0,39],b2min:17,optimis:44,gnu:[],launcher:13,properti:[41,0,26],neal:41,sourceforg:[5,1,43,44],calcul:[],plot2d:43,make_cel:0,occas:13,gave:41,gamma_1:15,"_install_hint":24,spawn:[],ringel:2,disjoint:[0,3],kwarg:[45,0],sever:[],hong:0,descent:28,tmintmax:43,exthom:15,perform:[35,0,17,3,41,43],suggest:[1,43,7,44],make:[12,13,14,0,15,1,38,20,3,4,40,41,7,19,5,9,22,44,18],mayb:[25,41],figsiz:22,pariss:24,complex:[],split:[5,2,11,43],test_si:10,maximalib:[43,44],expr_2:43,expr_3:43,complet:[0,2,3,45,9,13,15,18,19,20,21,22,24,25,26,5,34,38,40,41,42,43,39],setwd:40,nil:[1,43,44],darwin8:32,hang:[5,1,38,43],max_startup_tim:[9,11],charactert:9,rais:[0,15,1,38,18,40,41,9,5,20,44,24,28],ribbonstableaux:42,is_rel:40,sage0_vers:19,techniqu:0,panaxiomel:[5,38],kept:[10,36],singulargbdefaultcontext:41,jmol:[],inherit:43,ungrammat:11,maximaelementfunct:1,greatest:[39,0],thi:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,30,31,32,34,35,36,38,39,40,41,42,43,44],ncsu:0,programm:22,jean:[43,1,2,20,11,44],linsolv:43,unchang:9,matrix_from_col_vec:[31,35],identifi:[9,39],just:[0,15,1,17,40,7,20,10,21,41],starstar:25,d_cell:0,four_ti_2:30,human:23,homeomorph:0,libgap:9,languag:[31,35,0,3],enlighten:0,mupadfunct:42,expos:[14,30],mix:10,numtheori:[18,24],had:[15,9,7,0,26],macdonald:42,fortran:[31,35],redsb:41,lawrenc:[2,11,7],els:[18,23,24],save:[],change_r:10,opt:43,applic:31,gregg:[18,24],preserv:[15,0],test_workspac:9,hammersholt:[12,30],fricasel:5,is_remot:11,background:[23,6],noclef:[5,38],lcm:21,lck:15,pi_150:39,measur:0,get_default:39,specif:[40,2,11],arbitrari:[25,15,1,17,41,9,20,21,44,28],manual:[1,41,40,20,3],stdout_to_str:44,minpoli:41,montgomeri:17,underli:[5,20,11,44,38],www:[12,25,0,27,1,16,17,18,40,36,41,30,20,9,24,45],right:[18,1,42,41,0],old:39,deal:[41,0],is_kashel:21,negat:0,interv:[23,17],maxim:[12,21],rgraphic:40,intern:[25,10,22,41,39],stdoutcontext:11,g_i:17,flatten:0,indirect:[15,9,41],successfulli:17,witti:0,raytrac:6,insensit:[18,1,38,5,24],"_groebner_basis_magma":15,collect:[],mpz_mod:17,princip:[15,21],subclass:[40,43],existenti:0,multipli:[10,17],numbertheori:7,condit:[34,27,40,9,33,43],foo:[15,0],setdefaultrealfieldprecis:15,localhost:17,core:[31,20,25],plu:7,uncompress:6,"_local_tmpfil":[2,11],semicircl:0,confer:7,chapter:13,ip_form:15,alexand:[12,20,17],would:[0,26,15,1,38,18,40,5,10,43,44,24],magmagbdefaultcontext:15,slightli:[18,32,39,24,19],unfortun:[15,1,13,9],"42y":17,bug_report:43,size_in_byt:9,commit:41,attrib:41,eick:20,marshal:[10,14,30],singular_consol:41,ppi:30,"float":[43,15,1,2,38,7,5,10,11,39,41],bound:[15,17,28,0],ppm:6,wrap:[43,25,2,39,7,20,9,21,44],precomput:36,maple_consol:18,wai:[13,0,15,1,2,38,17,18,40,7,19,5,20,44,24,41],bioinformat:40,support:[21,0,15,2,38,40,6,7,20,9,33,11,44,24,41],qepcad_formula:0,transform:[],why:[15,21,41,43],avail:[13,35,32,0,34,15,38,3,18,5,7,20,31,9,42,21,22,39,24,40],gif:22,reli:44,coroot:15,fraction:[],gap_dir:9,call:[0,1,2,3,31,6,7,9,11,13,32,15,17,19,20,21,22,23,28,25,30,5,38,39,40,41,33,43,44],lowest:[18,24],bert:3,xy4:25,xy6:25,offer:[25,15,41,20,9,21],forc:[15,17,41],reduce_load_maximaabstract_funct:43,"2y6":25,pp1:17,multiprocessor:6,fricas_consol:5,"true":[0,1,2,3,4,6,7,8,9,10,11,12,32,15,17,18,19,20,21,22,23,24,25,26,30,5,33,34,36,37,38,39,40,41,42,43,44],reset:[4,9,18,8],slist2:7,moveto:22,prplen:17,new_nam:2,musik:[18,24],gen_nam:15,tell:[0,2,41,9,22,39],mersennewiki:17,featur:[12,18,24],semicolon:[18,41,24],classic:[25,44],zeta_ptsx:43,"abstract":[],one_curv:17,exist:[32,0,15,2,17,9,22],lie_vers:3,zeta_ptsi:43,wrongwai:36,komei:14,check:[0,27,23,38,40,41,5,9,22,44],password:19,floor:21,when:[34,25,0,26,15,2,28,17,3,18,40,7,20,9,33,11,24,41],refactor:9,mutablelist:25,qring:41,"3xy2":25,tie:44,degreerank:25,set_truth_valu:0,testimag:22,intend:0,rmodul:15,"15y":17,count_ellips:0,gap_reset_workspac:9,mlist:[7,44],intens:35,consid:[15,0],omega:42,is_axiomel:38,faster:[12,35,2,17,18,41,21,44],objgen:15,pseudo:[13,23],gforg:17,ignor:[12,21,25,0,26,15,40,36,41,19,9,33,11,44],time:[0,2,7,8,9,11,13,15,17,18,19,20,23,24,36,26,27,34,40,41,43,39],backward:[9,41],mpfr:27,breadth:17,concept:[],skip:28,global:[15,40,41],datum:41,focus:3,invent:14,functionel:[39,15,1,38,3,18,40,7,19,9,42,11,33,24,41],signific:33,calculu:44,per:[18,38,29,24],computation:35,guava:9,row:30,millisecond:0,depend:[32,26,2,17,40,41,19,42,11,44,24],graph:[4,1,43,32],decim:[17,28,0,39],intermedi:[27,9,10,41],start_clean:16,isgroup:20,axiomexpectfunct:38,retri:28,jvm:22,mapleel:18,stdfglm:41,isinst:[43,44],minc_tid:27,sourc:[12,0,3,18,40,21,24],string:[0,1,2,3,4,5,6,7,9,10,32,15,17,18,19,20,21,22,23,24,25,27,28,31,34,35,37,38,39,40,41,42,43,44],"_interface_init_":31,vdim:41,word:39,exact:[5,13,38,0,19],cool:10,self_out_file_cont:10,zeta_ptsx1:43,solver:[],did:[15,2,0],die:23,gui:[22,19],dig:27,iter:0,item:[15,21],div:[15,27,21,7],round:39,dir:[15,1,40,7,43,44],prevent:[18,20],work:[0,1,3,31,7,8,9,14,15,18,20,35,25,26,30,5,32,34,21,38,40,41,33,43,39],slower:[13,24],sr_sum:44,add_:21,htm:[27,41],sign:[30,0],"____":18,grdevic:40,volkmar:20,appear:[32,40,15,1,27,20,22],get_real_precis:39,mathematicafunctionel:7,anywai:44,current:[0,23,31,7,9,10,11,12,15,17,18,20,21,24,26,5,34,35,38,39,40,41,43,44],suspect:17,rubiksourc:36,magmagblogprettyprint:15,reduce_load_lisp:33,expect_peek:23,deriv:[43,32,27,2,11,44,24],gener:[],coeffici:[18,40,24,0,41],sol_class:10,french:[1,43,44],explicitli:[9,41,39],modif:38,address:[9,19],wait:[34,23,36,7,41],cartan_typ:3,"21645e":32,exact1:0,trial:[17,0],behav:20,extrem:[36,43,17,41],weird:15,digamma:[18,24],reclaim:0,ourselv:0,mobiu:43,primarydecomposit:25,extra:[25,0,27,6,10,28],modul:[13,0,15,27,41,20,22],kedlaya:[25,7],gnuplot_consol:4,and_:0,"1st":[40,43],instal:[0,3,7,9,13,32,15,18,20,35,22,24,25,30,31,34,21,37,40,41,42,39],should:[0,1,2,7,8,9,10,12,32,15,17,18,19,20,22,28,41,27,31,39,40,24,43,44],frobbi:[],get_variable_list:10,franco:[9,20],memori:[15,17,41,19,9,43],count_circl:0,max_to_sr:44,term_ord:41,prec:39,impos:43,live:41,handler:9,scope:11,cas_setup:24,peopl:[20,17,0],finit:[12,9,25,41,0],enhanc:7,visual:0,listattribut:15,templat:3,vmax:43,obj:[43,39,15,1,2,3,18,40,33,7,19,9,42,11,44,24,41],pov_fil:45,easiest:44,graphic:[40,10,7],ibm:[18,38],pretend:11,uniqu:[12,44,0],trang:[43,32],argspec:41,groebner_basi:15,whatev:13,purpos:[1,23,38,3,5,43,44],schoenemann:41,reduce_load_li:3,nearest:39,factint:9,unassign:21,curri:18,backslash:[9,21,13],topic:[9,20],crazi:10,abort:6,get_using_fil:[2,3],sharp:25,usna:0,expectfunct:[25,0,39,15,1,38,3,18,40,7,9,42,11,33,24,41],occur:[15,1,38,18,5,24],nearli:15,alwai:[34,0,1,18,41,9,39,24],sundai:38,intnum:[43,39],multipl:[],winter:36,ecl:[33,43,44],robidoux:0,write:[14,40,15,2,16,3,18,27,29,41,30,24],consist:[25,15,1,38,40,7,5],rubik:[],tild:40,maximaabstractfunct:[1,43,44],lehrstuhl:20,inputr:10,map:[15,21,0],product:17,mat:[30,3],atan:[27,43],max:[40,43,24],usabl:30,mnich:20,lenstra:17,canonicalize_rad:44,underscor:[21,25,0],data:[],"18x13y2":41,johnson:0,apropo:25,stdin:17,frica:[],produc:[0,15,18,27,7,20,9,41],is_jvm_avail:22,inform:[34,0,3,40,33,19,31,10,43,44,24],"switch":[20,43],preced:28,combin:[17,7,0],block:[34,15,6,41,9,11],subexpressions_list:27,ordinari:43,michel:20,tty:[13,23],zmax:4,sing_19:41,singular_vers:41,eval_using_file_cutoff:[9,11],set_precis:[43,39],still:[34,14,8,40,19,9,10,11],mainli:41,no1:25,dynam:[2,25],conjunct:0,group:[38,43,15,1,23,16,17,3,39,20,9,21,44],maximafunctionel:1,"_check_valid":11,jim:17,toru:43,platform:[40,22,19],window:[22,6,21,7,32],main:12,xyz:41,non:[13,25,0,26,1,2,34,17,41,11],bischop:20,factorinteg:7,get_verbos:15,initi:[12,43,36,0,39,15,1,2,17,44,18,27,30,31,9,11,22,23,24],sol:[10,36,44],nox:[5,38],d_witness_list:0,half:19,nov:41,now:[12,14,0,15,20,18,7,19,9,44,24],discuss:[18,1,24,0],nor:17,introduct:[],term:[18,27,10,41,24],name:[0,1,2,3,5,7,9,10,11,12,32,15,16,18,19,20,21,23,24,25,26,27,29,30,31,33,35,38,39,40,41,42,43,44],infinitely_mani:0,ifactor:[18,24],package_nam:40,separ:[15,2,18,40,28,20,9,43,24],januari:[38,3],updat:[39,0],compil:[27,38,39],domain:44,help_search:21,wiedemann:42,replac:[4,0],besch:20,continu:[],redistribut:[40,33],intrins:15,ispermgroup:20,resourc:40,happen:[34,40,19],kash3_osx:21,reid:36,accomplish:13,"3rd":40,space:[15,9,25,0,19],internet:[37,40,22],formula:0,correct:[18,40,22,44],nofil:11,earlier:[0,3],reduce_load_frica:5,pow_mc_c:27,ibar:41,runtimeerror:[15,1,38,18,6,41,9,5,20,44,24,28],bfloat:1,gap3:[],gap4:9,theori:[43,15,1,38,3,18,9,21,44,24],carl:0,modularform:15,ratdisrep:44,"byte":[31,39],care:[7,0],chevi:[9,20],or_:0,primitive_root:39,suffici:40,strlocaldata:15,question:[1,43,44,0],prescrib:3,rule:[44,0],"10mb":39,synchron:[40,11],recov:0,ripol:33,kociemba:36,place:21,imposs:[12,39],first:[],oper:[12,25,0,27,1,3,40,20],directli:[13,0,15,1,17,3,6,20,9,43,44,24],psageel:26,arrai:[43,30,0,44],hilbert:[12,30],tableaux:42,multiplicative_gener:9,bradshaw:[1,43,36,44],ring:[12,14,0,15,2,3,18,25,7,9,10,43,24,41],open:[0,40,15,2,3,27,6,29,31,42],lexicograph:[15,41],size:[25,17,3,7,20,31,9,41],given:[0,1,2,3,4,5,6,7,9,10,13,32,15,16,18,19,20,21,24,25,26,27,28,31,33,34,35,36,37,38,39,40,41,42,43,44],unlink:[9,2,40,3],ellinit:[2,39],silent:[6,11],convent:[15,0],width:[40,25],pyobject_to_max:44,structure_sheaf:25,necessarili:40,circl:[43,0],summarydefault:40,conveni:[13,0],especi:13,copi:[13,25,0,26,15,2,40,19,43],do_clean:[9,11],specifi:[4,17,45,0,19],factor_digit:17,hypergeometr:[1,38,44,43],mqappli:44,than:[12,13,35,0,15,2,38,17,18,41,5,9,10,21,44,24],png:[4,40,6,22],serv:[9,41,13],fourti2:30,"9x16":41,aami:40,subexpress:27,is_run:[11,8],"_install_hints_ssh":19,classified_solution_dict:10,were:[43,14,44,0],posit:[25,0,15,1,2,17,44,18,27,20,10,23,24],seri:[12,27,44,39],pre:[20,38],skip_2nd_desc:28,sai:[18,44,24,3],not_:0,current_ring_nam:41,argument:[21,25,5,0,40,15,2,38,17,27,45,41,19,31,11,44,24,43],residu:[10,17],attach_spec:15,prp:17,notimplementederror:[2,33,30,3],saw:0,sat:15,make_random_st:1,shtml:43,engin:[31,27,40],squar:[3,18,31,10,35,24],plot3d_parametr:[4,43],moreov:[15,1,38,17,43,44],consortium:31,note:[0,1,2,4,7,9,12,13,32,15,16,17,18,19,20,21,24,25,26,5,38,40,41,42,43,39],ideal:[],denomin:12,harald:40,take:[25,0,15,17,36,31,32,21,44],advis:40,interior:0,intromax:1,noth:[13,15,2,44,41,9,11,23],realpath:40,begin:25,sure:[13,1,38,40,41,9,5,20,44],normal:[0,26,1,38,17,18,41,5,20,10,42,24],buffer:[13,23],sagemath:[9,41,32,20,19],compress:[6,39],list_attribut:15,beta:[15,18,32,39,24],stdhilb:41,uppercase_:[5,38],pair:[27,10,32],giacfunctionel:24,pager:[18,9,20],latex:[],quasihomogen:41,krandick:0,subinterv:43,later:[27,11,26],typeset:1,dodecahedron:22,crossov:41,runtim:[15,17],axi:[32,0],sigma:17,gracefulli:1,remove_rep:27,cygpath:22,show:[17,7,3],gap_packag:9,atom:0,subprocess:[14,26,23,19,9,11,22],max_to_str:44,demey:23,preciss:27,threshold:11,fifth:0,theissen:20,d_set:0,is_lock:26,onli:[35,32,0,15,23,17,20,40,7,8,31,9,10,21,44,28,41],slow:15,matlab_consol:35,transact:27,activ:[41,0],state:[13,36,0,1,41,8,9,11],parametr:[4,43],over:[12,25,0,15,1,38,17,18,7,30,19,10,21,24,41],startswith:[9,40],gap3_vers:20,variou:[31,15,36],get:[0,1,2,3,7,9,10,11,12,13,32,15,17,18,19,21,22,24,25,26,31,33,35,38,39,40,41,42,43,44],monografia36:27,reduce_load_maxima:1,lisser:3,repr:[9,1,25,7,8],autoload:40,mp_tide:27,cannot:[31,9,35],ssh:19,tgen:6,pipermail:1,laguna:9,gen:[12,25,15,2,41,19,21],requir:[13,35,25,0,43,37,40,31,32,21],embedd:33,prime:[12,34,15,17,41,9,21,28],vmin:43,randvar:44,median:40,yield:[32,1,38,17,41,5],mapcoeff:42,xmax:[4,43],scott:0,where:[25,0,15,1,28,17,3,18,40,7,30,9,10,43,22,24,41],vision:[],summari:[5,40,38],wiki:38,kernel:[15,39],genmatrix:1,assumpt:[44,0],qepcad_vers:0,interpreternam:2,infinit:[2,11,23,0,44],detect:[41,44],kei:[10,19],label:[25,0,3],hist:40,enough:21,use_fil:9,between:[43,36,0,15,23,20,18,40,41,19,9,10,11,44,24],giac:[],"import":[],spars:41,pretti:[1,44,0],parent:[0,1,2,3,31,7,9,11,32,15,18,19,20,21,24,25,26,5,33,35,38,39,40,41,42,43,44],screen:[9,21,17,43],cycl:14,init_list_length:[40,39],come:[40,0],reduce_load_axiom:38,reduce_load_matlab:35,magmafre:37,tmax:43,quiet:[17,28,8],tutori:[],seress:20,mani:[14,0,15,1,38,17,40,7,10,43,44,24],stacksiz:[39,8],get_solution_dict:10,interreduced_basi:41,pov:[],pow:27,pop:4,maxima_vers:43,exploit:10,werner:[20,0],colon:15,waldek:38,reduce_load_mupad:42,nicola:0,xdvi:1,poli:[20,10,17,41],rseek:40,caret:41,zimmermann:17,stat_model:40,marc:3,sample_point:0,invert:40,gutow:22,an_expr:43,mark:[41,0],qepcadfunct:0,nextprim:[15,21],valueerror:[0,8,17,20,9,11,44,28],arcsin:27,thousand:[13,32,15,1,38,17,7,5,9,39,41],resolut:[6,41],bmp:6,isprim:[18,21],workspac:9,matrix_integer_dens:3,apiec:0,thing:[13,0,18,40,20,24],those:[15,18,24,0,44],"case":[12,34,36,0,1,2,38,17,18,40,7,20,5,9,44,24,41],"__mod__":25,steinberg:0,is_magmael:15,pts_lst:43,maxima_consol:43,"_magic3x3":30,stdout:[9,11,22,44],download3:20,prenex:0,"100th":32,cluster:17,grevlex:25,ivp:27,solve_linear_system:32,shutil:27,ascii:[5,1,38,39],"__init__":9,gfan:14,develop:[39,15,1,38,3,41,43,44],intmod_gap_to_sag:9,same:[12,13,32,0,27,18,40,41,19,9,10,39,24],poincar:12,rectifi:18,binari:[25,27,1,43,44,24],html:[36,0,1,18,40,7,20,21,44,24,41],lispfunctionel:33,"_eval_lin":[1,11,43,44,9],document:[12,43,0,15,1,38,40,7,30,21,44,24,41],fundamental_discrimin:15,finish:[9,24,0,26],start_filenam:10,nest:11,axiomel:38,masami:33,capabl:[40,41],"_aa":21,improv:[25,1,2,40,33,43,44],extern:[7,19],immedi:[18,23,7,24,26],defn:[1,43,44],vkcurv:20,mxn:32,is_maximael:1,appropri:[15,18,21,41],grp:21,singmast:36,kashel:21,rationalfield:15,directproduct:20,without:[0,37,1,40,7,44,41],greuel:41,nfun:27,ujf:24,roughli:[24,3],ltype:0,polygen:0,execut:[0,26,2,39,6,31,20,11,22,44],among:0,excel:[1,38,7],resp:[32,41],e641001f8b8d1129:44,start_from:10,kill:[23,39,33,41,8],insight:0,install_packag:40,mqapply_to_sag:44,hint:19,o39:25,except:[0,15,1,23,38,3,18,41,20,5,9,24,28],param:15,remote_clean:[9,11,19],real:[],psi:[18,44,24],around:[],onscreen:[1,6,44],read:[],outermost:0,sage_getsourc:[15,41],test:[0,1,3,4,31,6,7,9,10,13,32,15,17,18,19,20,35,24,25,27,28,5,33,38,39,40,41,42,43,44],"21d":17,grid:[1,43,40],is_na:40,world:23,m3370:[18,24],mod:[9,17,39],terminal_echo:[9,11],read_data:29,intel:18,whitespac:28,npolynomialr:25,ascii_art:7,integ:[],server:[0,1,3,31,7,9,11,32,15,18,19,21,28,41,25,5,33,35,38,40,24,42,39],either:[0,17,4,40,41,10,43],min_tid:27,output:[],inter:20,manag:11,paixao:31,node:3,helpexpress:40,polylog:44,rngintelt:15,simplici:12,isosampl:4,magma:[],mathematica_consol:7,revisit:0,images:7,nonzero:[10,0],freez:15,saliola:[9,20],mutablehasht:25,qiang:45,definit:[],mathematicael:7,maximaabstractel:[1,43,44],allow_use_fil:11,exit:[35,32,0,26,2,8,31,11,43],cylindr:0,base_r:[25,41],torsion:28,complic:[],refer:[15,27,0,40],polyev:17,besselk:[32,7],besselj:32,sagespawn:23,power:[34,25,17,44,31,39],asap:32,bivari:0,garbag:[],ration:[],"9x6y4":41,gp_version:39,sage2scilab_matrix_str:31,broken:14,great:26,fulli:[41,0],regexp:25,"throw":39,old_opt:41,celler:20,src:20,stone:6,central:9,greatli:[1,38,44,43],worksheet:9,joyner:[35,32,43,1,39,41,9,21,44],acm:27,fauger:15,degre:[25,0,15,7,20,41],eigenvalu:1,input_r:10,stand:0,acz:27,singnot:36,routin:[32,0],effici:[39,0],tides_prec:27,elementari:0,fouss:17,invers:[32,39],strip:[21,25,0,26,15,43,3,37,33,7,19,9,42,11,44,24,41],insuffici:0,d_true_cel:0,your:[13,35,25,0,32,15,20,3,18,37,45,7,30,19,31,9,42,21,39,24,41],extcod:15,kruppa:17,ymax:[4,43],qepcad_formula_factori:0,set_r:41,overwrit:2,prepars:19,start:[0,1,2,9,10,11,13,15,16,18,19,20,23,28,36,26,31,34,38,39,40,24,43,44],again:[15,11,41,0],low:[32,0],lot:[15,10],svn:39,programmat:0,verbatim:41,linalg:[18,42],tupl:[],jul:39,mlist_to_sag:44,cutrel:7,satur:28,to_poly_solv:44,prpval:17,longer:[9,11,17,20,8],notat:[43,14,1,2,38,40,5,36,33,11],tripl:43,"18x3y6":41,possibl:[18,25,0,2,38,28,3,4,40,6,7,31,33,43,44,24,41],"default":[0,2,4,6,8,9,10,11,15,17,18,20,21,22,23,24,25,28,34,38,39,40,41,43,44],nintegr:43,homotopi:10,miguel:27,sylowsubgroup:20,pulp:16,eigenvector:1,connect:[40,0],phc_object:10,taylor:[27,1,44,39],sec323:41,creat:[0,1,3,6,7,9,15,17,18,19,21,22,28,41,25,27,5,34,38,39,40,24,43,44],sectio:20,certain:[40,33,17,7],felix:[2,11,7],intro:40,file:[],umax:43,allow_multi:0,"0000e":35,denot:15,incorrectli:44,image_typ:22,mathematik:[20,41],selfattrnam:15,mathematica:[],orient:[2,33],field:[],gap_cmd:9,valid:[15,9,28,0,39],collis:10,writabl:15,geometr:0,you:[0,1,2,3,7,9,13,32,15,17,18,19,20,21,22,24,25,26,30,31,33,34,35,40,41,42,43,39,45],architectur:9,fork:[5,2,11,38,8],nedergaard:14,org:[32,27,38,17,40,36,41,20,9,24,45],docstr:[41,0],polynomi:[],track:10,pool:9,reduc:[18,17,41,24],unbind:[9,20],available_packag:40,nobase2:17,directori:[43,15,40,7,30,9,35,39],descript:[18,6,24,0],tricki:9,rootdatum:15,laplac:[],zmodnzobj:9,attardi:33,sage_getargspec:41,cpu:[34,15,2,18,41,20,9,43,24],disp:44,represent:[25,0,39,15,1,2,38,3,40,41,9,43,44],all:[0,2,3,8,9,10,11,12,15,17,18,21,24,25,26,5,34,38,39,40,41,42,43,44],archive_nam:22,"318491487l":2,drideout:[18,24],osx:[40,21],illustr:[26,15,1,41,9,21,39],"_expect":11,prplog:17,defaultdirectori:22,octave_vers:32,disc:9,deprecationwarn:[9,41],follow:[0,1,3,31,7,8,9,32,15,17,18,20,35,28,41,5,34,21,38,39,40,24,43,44],disk:[15,38,18,40,43,24],sage_global_r:41,children:0,felsch:20,dot_product:40,albrecht:41,mathematicafunct:7,program:[12,13,35,14,0,34,15,28,17,3,18,6,7,30,31,32,10,21,24,43],get_failur:10,hasattr:2,rstrip:22,ylabel:4,numberfield:15,fukuda:14,thursdai:5,sound:10,liter:[21,17],jensen:14,straightforward:21,trivialsubgroup:20,far:[1,36,34],liefunctionel:3,roe:25,util:40,candid:17,fan:[],fall:44,veri:[13,43,32,0,26,15,1,38,17,39,6,7,5,9,21,44,41],fac:[9,0],ticket:[12,32,27,1,23,40,41,9,20,44],realpart:[1,44],r_consol:40,dimensionsloewyfactor:20,harri:41,lisp:[],tides_rnd:27,list:[],datafile_cmd:22,lieelement:3,reduce_load_macaulay2:25,adjust:0,form:[0,15,1,27,7,10,43,28],stderr:[9,22],small:[34,2,17],grenobl:24,snapshot:34,dimens:[12,25,0,15,41,19],maximaabstractfunctionel:[1,43,44],ten:[32,15,1,7,9,39],start_si:10,tex:1,range2:4,zero:[12,0,15,1,40,41,44],design:[12,9],pass:[12,0,15,2,17,4,40,6,45,19,20,11,28],further:[34,44,41,3],"_gap_init_":9,what:[12,34,0,15,38,40,6,7,5,9,10,22,44,41],abc:[15,9,41,39],sub:[25,15,18,41,10,11],richard:0,clock:39,sum:[12,1,38,40,5,10,44,24],abl:[40,7,9,21,44,41],brief:40,delet:[15,17,41],version:[0,1,2,3,5,6,7,9,10,11,12,14,15,18,19,20,21,22,23,24,25,30,31,32,33,34,35,38,39,40,41,42,43,44],intersect:[12,41,0],eaton:32,"1lcd":22,polgaloi:39,method:[],contrast:13,get_precis:39,leeuwen:3,full:[13,0,15,22,44,24],hash:9,v3r4p0:20,v3r4p4:20,infin:[10,43,44,24],modular:15,disjunct:0,solari:40,excess:43,grape:9,parenthesi:[31,35],modifi:[14,0,38,32,40,5,9],mult:41,path_track:10,search:[13,36,15,18,40,28,24],read_matrix:30,divisor:39,linal:42,indetermin:9,prior:[17,44],amount:[37,38,17,18,41,20,9,43,24],doctest:[15,17,40,6,41,30,8,9,22],pick:[15,0],action:12,symmetricfunct:42,not_a_real_qepcad_quantifi:0,y10:40,quotient:[15,25,41,44],via:[34,14,1,38,40,25,41,9,5,20,10,11],primit:[40,0],implic:0,filenam:[15,2,17,3,40,6,7,30,9,10,22,45],strip_answ:35,abeliangroup:15,coercion:[15,10,41],select:[31,40,0],goetz:20,ring_nam:41,povrai:45,distinct:[15,34],selmer:28,ctrl:[32,15,2,38,18,40,5,9,24],s_list:10,two:[18,40,32,0,26,15,23,38,17,4,27,7,19,9,21,39,24,43],coverag:22,asm:17,realfield:29,taken:[0,3],minor:[15,38,41,30],more:[13,43,14,0,15,2,38,17,32,18,40,7,20,5,9,21,22,44,24,41],memcel:0,desir:[27,9,10,43,0],hundr:31,probabilist:17,function_nam:[40,2,21],flag:17,particular:[0,27,2,7,21,41],known:[40,17,0],cach:[43,0,15,2,38,40,9,11],ronan:31,none:[0,1,2,3,4,5,7,9,10,11,32,15,17,18,19,20,21,23,24,25,26,27,28,30,31,33,35,38,39,40,41,42,43,44],endpoint:[10,43],blah:39,der:41,all_cel:0,det:41,optimalsolv:36,dev:40,histori:[31,13,35,32,7],erfinv:32,del:[15,1,41],dem:43,r2006a:35,dec:9,def:[41,7,0,3],fougeron:17,prompt:[21,25,26,28,18,35,41,9,11,24,43],substanti:36,brown:0,rodriguez:27,share:[21,39,24,43],datafil:[22,39],accept:14,sphere:6,permgroup:9,saved_expect:11,explor:0,bjark:[12,30],sec26:41,huge:[2,38],cours:[41,0],mai:[13,36,0,1,2,4,6,20,9,11,44],newlin:[15,9,21,25],awkward:1,divid:[18,17,0],rather:[15,11,41,0],anoth:[18,43,32,0,13,1,4,41,19,31,35,44,24],suyama:17,mapl:[],divis:[18,17,44],clean_output:7,simpl:[12,0,1,38,17,3,40,41,5,20,44],sage_env:15,algebra:[43,25,0,15,1,38,3,41,5,42,21,44,24],minimum:7,par:27,plane:[10,0],"3y7":25,maximalibfunctionel:44,monografiaspublicada:27,iseven:21,"3y8":25,associ:[12,13],"short":[17,41,28],kash_consol:21,qepcad_expect:0,confus:8,author:[0,1,2,3,5,6,7,9,10,11,12,14,15,17,18,20,21,22,23,24,25,27,30,31,32,33,35,36,38,39,40,41,42,43,44,45],my_packag:9,caus:41,matrixspac:[31,35,32],volum:10,juergen:20,multivari:[12,25,15,3,7,9,10,44,41],help:[],itd:27,mdiff_to_sag:44,held:0,i386:32,paper:12,through:[],left:[15,1,0],connected_subset:0,paramet:[],"9x12y3":41,style:[15,7],render:[6,45],gcfactor:43,resort:[18,24],parse_max_str:44,conjugatesubgroup:20,might:[34,11,7],reduce_load_kash:21,dynkin:3,"return":[],maxima_calculu:44,dim:41,timestamp:[5,38,17],inria:[31,17],collin:0,withsb:41,detach:11,mpolynomi:41,bigger:[5,1,38],varianc:40,kbase:41,blesa:27,eventu:[23,36],indeterminatesofpolynomialr:9,alg924:27,mathematician:3,dik:36,unlik:[9,21,3],mysteri:15,iff:0,compris:0,found:[34,36,0,17,40,5,20,21],slist:7,weight:[15,41,3],reduce_load_gap:9,b2max:17,idea:[1,41],procedur:[12,15,18],realli:[17,10,14,44,0],katom:42,x2y3:25,x2y2:[25,41],magma_consol:15,expect:[0,1,2,3,7,8,9,11,32,15,17,18,19,20,21,23,24,25,26,28,31,33,35,38,40,41,42,39],utexa:1,hart:[],todo:[],reduct:[17,41,3],znlog:39,robert:[1,43,36,44],start_filename_or_str:10,"4pi":7,research:0,max_level:0,isrec:20,print:[0,1,3,4,31,6,7,9,10,11,15,17,18,20,21,22,24,25,26,28,5,34,35,38,39,40,41,43,44],hilb:41,get_docstr:41,unparsed_input_form:38,unitgroup:21,singularfunct:41,driver:27,differ:[1,2,7,9,36,10,12,13,17,18,19,20,21,24,25,5,38,44,40,41,43,39],labl:25,is_expectel:11,reason:[21,36,41,0],base:[0,1,2,3,4,5,6,7,8,9,11,14,15,17,18,19,20,21,22,23,24,25,26,27,28,30,31,32,33,35,37,38,39,40,41,42,43,44],put:[0,15,2,38,18,22,24],fricasexpectfunct:5,basi:[15,21,41,30],thread:44,launch:[20,7],monografia:27,dir_:15,lie_consol:3,get_classified_solution_dict:10,circuit:30,integrand:43,major:15,oserror:23,notifi:25,upper:[43,28,0],misc:[15,2,38,27,41,22],number:[],placehold:17,maximum_num_subinterv:43,start_sav:10,giacfunct:24,done:[34,36,15,23,38,3,18,40,41,5,43,28,7],construct:[12,25,0,26,27,40,41,9],gnuplot_preambl:43,horribl:15,miss:[40,2,11],kill_spawned_job:8,gpl:[32,27,1,38,5,9,43,44,24],macaulay2funct:25,guess:17,vararg:41,interact:[],extra_tim:36,least:[34,0,15,41,9,43,44],tolab:27,classgroup:21,statement:[11,41],from_:40,store:[38,17,18,41,9,24],pierrick:17,de_solve_laplac:43,option:[0,2,3,4,31,6,7,10,12,32,15,17,18,19,20,21,22,24,25,28,30,5,34,35,37,38,40,41,42,43,44],zmodpzobj:9,similarli:17,scifac:42,pari:[],part:[43,0,30,9,10,21],pars:[1,43,25,44,0],dirichletgroup:15,consult:0,"_______________________________________________________":20,cosh:44,std:41,king:[2,11,41],level:[36,0,15,6,41,31,33,35,39],cyclic:[15,41],remot:[39,19],breuer:20,remov:[35,25,27,40,9,21,24],horizont:32,remove_output_label:25,path_track_fil:10,str:[34,25,37,1,2,28,3,18,40,6,7,20,9,10,43,24],multigrad:12,script_subdirectori:[21,25,32,15,1,38,39,3,18,5,35,7,31,9,42,11,40,33,24,41],randomli:18,cleaner:[],comput:[],"4ti2":[],"5236600000000002e":32,macaulai:[25,41],"20121933088197564152489730020812442785204843859314941221237124017312418754011041266612384955016056b1":1,rplot001:40,packag:[12,35,25,0,32,15,44,3,18,40,7,30,20,31,9,10,21,42,24],mupad:[],reduce_load_sag:19,dedic:43,"null":[27,40],psage:26,lie:[],sage2octave_matrix_str:32,built:[12,25,0,15,3,40],equival:[12,7,0],randint:26,self:[43,25,15,2,38,3,40,41,10,11,24],also:[0,1,3,4,31,7,9,10,12,13,15,17,18,20,24,27,5,34,38,40,41,33,43],accessor:0,restart_on_ctrlc:[9,11,21],build:[38,17,0],jacobian:41,"_r_class":40,wait_for_prompt:9,gaudri:17,n42:29,distribut:[27,40,43,3],gauss_col:41,previou:15,sage_matrix:41,unappli:24,most:[39,14,0,40,15,1,2,17,3,37,6,41,30,20,31,9,33,11,44,28],selmer_onli:28,cygwin:[22,7],alpha:[15,18,24,0],model:[40,6],"16mb":21,maxread:[21,25,0,32,15,39,3,18,35,7,31,9,42,11,40,33,24,41],clear:[43,32,15,1,2,18,41,19,9,11,44,24],cover:0,dimension:[1,10,0],attachspec:15,ext:22,halllittlewood:42,exp:[43,27,1,7,33,21,44,24],eisen:15,scilab:[],hhong:0,as_typ:38,cdf:10,intvec_express:41,gap3el:20,nokei:43,sage_flattened_str_list:41,"3x2":41,session:[1,3,31,7,8,9,11,13,32,15,18,19,20,21,24,25,5,33,35,38,40,41,42,43,39],particularli:[20,17,0],x____x:39,tachyon_rt:6,"_sage_":[15,40,2,11,7],find:[34,36,0,17,7,43,24],universitaet:41,impact:15,cell:[40,22,0],schoenert:20,coerc:[15,10,29],indexerror:15,abad:27,copyright:[32,40,27,38,18,5,31,9,42,35,33],slowli:[23,43],is_gapel:9,pi_def:39,solut:[1,10,32,0,36],comparison:[1,43,41,44],factor:[],temp_project:30,maximalord:[15,21],abelian:21,hit:[5,1,21,38],unus:41,express:[13,43,25,0,15,1,38,17,18,27,7,20,5,9,21,44,24,41],kind:[15,32,0],jeroen:23,nativ:[22,7,3],maximalibel:[43,44],rest:[5,1,38],banner:[28,0],testplatformequival:40,restart:[40,25,41,28],kty:21,abs_integr:44,whenev:[15,18,24,0],bar_cal:15,dilog:18,eq1:7,common:[],d_false_cel:0,wrote:[12,17,14],withr:41,set:[0,1,2,3,7,9,12,32,15,17,18,19,35,22,24,25,26,28,31,33,21,38,39,40,41,42,43,44],art:[5,1,38],dump:[43,25,15,38,39,40,41,19,9,33,21,44,7],sep:[40,3],startup:[36,0,2,31,9,11],decompos:[12,0],see:[0,1,2,6,7,9,36,10,11,12,13,32,15,17,18,19,20,23,24,25,30,38,39,40,41,33,43,44],data_to_list:34,kiran:[25,7],arg:[43,25,44,15,1,2,38,3,18,40,7,31,9,33,21,23,41],close:[21,27,23,3,40,29,41,11,2],pm1:17,someth:[0,15,2,17,4,41,30,9,21],won:[9,40],clisp:38,nontrivi:9,subscript:0,altern:[15,13,21,0,20],signatur:[15,21],addcol:42,maximaabstract:[1,43,44],web:[15,22],numer:[],complement:12,isol:10,incident:[18,24],outfil:[6,45],ipython:15,prptmp:17,sageel:[26,19],vectorspac:[15,32],miscellan:[],ntick:43,both:[13,41,0],last:[0,39,15,1,2,17,3,40,6,41,30,20,31,9,33,11,44,28],delimit:25,cubex:36,set_verbos:[15,41],foreign:[2,11],undetermin:0,singular_gb_standard_opt:41,forgotten:44,attrnam:[15,2],tangent:0,whole:[15,9,11],pdb:22,de_solv:43,load:[],simpli:[2,40,6,7,9,44],point:[39,0,26,15,38,17,3,4,41,5,9,10,43,44,24,28],instanti:[43,44],original_workspac:9,arbitrarili:0,issac04:0,tga:6,suppli:7,zeta:43,simpler:[7,0],"_keyboard_interrupt":20,java:22,stamp:17,devic:[15,40,41],due:6,gapfunct:9,implicit:15,axiom_consol:38,reformat:[11,44],tmpfrts_var_t:27,verticallist:25,strategi:41,sage_rat:44,ram:37,imag:[],convert:[34,15,38,3,40,41,30,5,9,43,44,28,7],gap:[],coordin:[0,3],testinheritedmethod:40,maplefunctionel:18,understand:[41,0],save_workspac:9,func:[15,41],binomi:44,test_gap_dir:9,my_vector2:[31,35,32],look:[25,0,23,18,39,24],my_vector1:[31,35,32],set_se:[32,15,1,2,40,41,31,9,39],mplu:44,bill:[],parent_bas:2,sobj:7,formatt:[9,21],"while":[34,0,23,38,5,9],unifi:[13,19],abov:[0,1,18,7,8,21,24],error:[43,32,0,15,1,38,39,18,5,6,41,20,31,9,21,22,44,24,28],fun:[1,43],loop:[23,17,7,20,11,2],earli:[34,0],readi:36,jpg:[16,22],echelon:[15,1],itself:[15,17,18,40,7,19,21,44],cascmd_en:24,quadrat:[],rid:[2,11,25],maximalibelementfunct:44,octav:[],irrelev:14,minim:[12,25,30],extra_opt:6,withdim:41,funni:[15,13],spawned_process:16,decom:12,"__repr__":40,mupkern:42,appreci:38,x86:39,globalenv:40,optim:[20,17,36],wherea:[18,2],zeta_ptsy1:43,temporari:[11,39],user:[34,25,15,1,3,27,41,22,44],robust:[43,32,15,1,39,41,9,21,44,7],provabl:[18,17],typic:[],recent:[0,39,15,1,2,17,3,40,6,41,30,20,31,9,33,11,44,28],mobj:7,lower:[43,17,0],task:35,lib:[9,2,44,41,20],simplicial_complex:12,"9y8":41,entri:[35,32,27,1,40,41,31,21,28],pickl:[25,2,40,41,19,9],treefil:17,set_real_precis:39,normalclosur:20,sageobj:40,positiveinteg:[5,38],is_lieel:3,testvirtu:40,relement:40,simp:44,a_2:0,maximael:[1,43,8],export_imag:22,save_as_start:10,"337811y":17,split_lin:[9,11],combinat:[18,42],saved_start:10,user_config:15,cut:25,pts1:43,is_loc:11,pts2:43,theoret:3,rgb:6,ratsimp:1,input:[],subsequ:[9,43],ringlist:41,useless:[15,41],bin:[9,11,20,0,8],marco:27,abcabc:25,format:[1,6,7,30,19,43,22,28],big:9,asciiartstr:[9,2,7],inequ:0,poincarehomologythreespher:12,"76h":17,kash:[],insert:[9,21],bit:[32,17,6,7,43,39,41],characterist:41,is_maximalibel:44,formal:1,ptsy:43,ptsx:43,parentwithbas:2,jokela:10,signal:[23,8],use_pag:6,resolv:36,elaps:15,ptsi:43,max_at_to_sag:44,project_:30,ptsn:43,mpolynomial_libsingular:3,bruin:[1,43,44],encount:43,often:[36,0,38,41,9,10,11],sage14:21,creation:[25,15,32,41,9,21],some:[],back:[39,25,0,26,15,3,18,7,32,43,44,24,41],emph:26,trait_nam:[25,0,39,15,38,20,3,18,40,7,19,9,42,43,33,24,41],"_root_":0,"95mb":15,sampl:[4,40,0],sprint:[21,25,38],surpris:0,brent:17,scale:[22,17],lllbase:25,prot:15,id0:12,id1:12,schelter:43,substitut:[43,25,0],mathemat:[31,27,17],larg:[12,15,17,7,10,21,39],proj:25,maxima_abstract:[1,43,44],prod:12,proc:[18,24],foundnumb:17,machin:[22,39,19],run:[0,2,3,6,7,8,9,10,11,13,15,17,18,19,22,23,24,36,26,30,5,34,38,40,41,43,39],realprecis:39,lispel:33,lispfunct:33,step:[27,9,17,0,22],feb:[31,9,20],octave_consol:32,hulpk:20,ncol:[41,30],lr_tensor:3,constraint:44,transpos:25,normalintersect:20,plai:0,longwithunderscore314159:0,solution_extens:0,idl:[17,26],gnuplot_term:43,gamma:[1,43,32,44,24],univers:0,primarili:[40,25,41],within:[11,7,0,41],phase:0,ensur:11,fpprec:1,convert_r_list:40,invalidate_al:8,inclus:25,span:13,socl:12,combinator:[15,9,18],fast:[],custom:[15,40],"9x10y4":41,subst:[5,1,38,43],includ:[13,25,0,15,1,38,17,18,27,6,7,30,31,9,10,43,44,41],forward:2,properli:[11,22],conjugacyclassestri:20,rubikscub:36,gfan_substitut:14,decomposit:[12,43,0],pwd:[15,35],link:[27,1,38,40,20,43,44,24],translat:[],newer:43,delta:[27,1],mysqcu:[18,24],line:[0,3,31,6,7,9,10,11,13,32,15,16,18,19,20,21,24,25,29,5,33,34,38,39,40,41,42,43,44],sr_limit:44,info:[4,15,28],testgf9:41,z54:44,commut:25,function_cal:[15,2,3,40,9,33],server_tmpdir:[21,25,40,15,39,38,28,32,18,5,35,7,19,31,9,42,11,33,24,41],readlin:[0,27,38,7,5,9,39],is_macaulay2el:25,similar:[13,44,0,40],sr_tlimit:44,curv:[],constant:[27,17,7,0],valu:[],parser:6,doesn:[0,15,1,23,7,9,21,22],repres:[32,0,1,18,40,30,43,44,28],"char":[25,41],is_nan:40,incomplet:32,magmaexpr:37,addrow:42,home:9,pfister:41,remove_const:27,gnuplot:[],titl:4,nan:[40,35],invalid:[6,41,8,31,9,43,28],nam:31,bracket:[43,0,1,3,31,35,44],vrang:43,new_prec:39,tempdir:27,gro:30,enpc:31,nice:[14,0,1,17,40,21],draw:[4,10],clean:[40,25],magmael:15,polynomialr:[12,25,15,7,9,10,41],william:[1,2,3,7,9,10,11,14,15,18,21,24,25,31,32,42,35,38,39,40,41,33,43,44],gap3_consol:20,eval:[1,2,3,31,7,8,9,11,32,15,18,19,21,24,25,26,28,5,33,35,37,38,39,40,41,42,43,44],magma_free_ev:37,lang:24,algorithm:[12,14,15,1,38,17,39,27,36,43,44],rand_se:2,hsplit:15,notion:25,discrimin:21,depth:17,"95m":17,came:0,onc:[36,0,3,40,9,11,44,28],hello:[15,5,23,38,25],hampton:[10,14,30],code:[2,3,31,7,9,11,15,17,18,19,21,24,25,26,30,5,33,37,38,39,40,41,42,43,44],partial:[43,0],zmin:4,plot_list:43,axiom4sag:38,ellips:0,ellipt:[],legal:44,edu:[15,1,25,0,36],withoff:7,"18x5y6":41,rfunctionel:40,multi_polynomial_libsingular:3,toric:[9,30],gap_command:9,simon:[2,11,41],graver:30,ulimit:[18,9,11],effort:38,rngupolelt:15,is_interfaceel:2,send:[25,1,23,7,19,9,21,44,24,41],qepcadcel:0,aris:15,new_with_bits_prec:39,de_system_plot:32,sent:[9,11,8],irreducible_decomposit:12,account:0,unit_quadratic_integ:43,row_vector1:[31,35],row_vector2:[31,35],magmafunct:15,implicitli:41,kcach:41,random_test:2,tri:[36,0,7,9,11,24],load_packag:[9,20],magic:[15,24],gettim:39,bessel:32,michael:36,"try":[12,25,15,1,23,38,17,18,40,41,20,5,9,43,44,24],race:9,loadlib:41,integra:24,pleas:[40,32],impli:0,smaller:41,readabl:[],besselh:32,natur:[44,0,3],getcid:0,focu:0,blanklin:[0,15,17,20,31,9,39],maplefunct:18,download:[20,21,24],isfil:9,odd:0,append:[6,17,21],compat:[38,41,5,9,11,44],index:[13,0,15,17,3,40,31,20,35,24],compar:15,fine:15,han:[20,24],m33:[31,35,32],affin:41,access:[0,2,3,18,40,7,20,9,10,44,24,41],fldratelt:15,experiment:[38,39],can:[0,1,2,3,5,7,9,10,12,13,14,15,17,18,19,20,21,22,24,25,26,27,30,31,34,38,40,41,33,43,44],radexpand:44,gc_disabl:11,tmp_dir:[27,9],despit:0,"_atnospam_":45,old_prec:39,use_workspace_cach:9,len:[12,0,15,38,39,18,40,19,9,10,43,42,24],bodi:0,tini:27,matrix_from_row_vec:[31,35],let:[36,0,18,7,20,9,24,41],sinh:1,lex:[25,14],sing:41,vertic:[0,3],sinc:[13,14,0,39,15,2,20,3,4,40,25,41,19,9,43,44,24,18],original_gap_dir:9,remark:[11,41,24],convers:[9,41,28,44],genu:[],macaulay2_consol:25,indmonogr36:27,"_name":[40,3],converg:43,rdf:41,qepcad:[],chang:[],cad:0,coercibl:15,jeremi:0,assign_nam:15,ansi:20,kash3:21,apr:20,appli:[21,41],approxim:[10,43,17],offset:3,foundat:40,submodul:15,siev:[],redc:17,"boolean":[43,0,17,41,10,11,22,44],archive_n:22,sgn:44,associated_prim:12,usg:20,reduce_load_el:19,from:[],zip:22,commun:[11,41],doubl:[27,40,41,19],next:[43,0,26,15,23,7,9,21,39,41],websit:[5,20,35],few:[5,38,26],chr:15,usr:[9,20],lisp_consol:33,nprint:[15,9],cran:40,jonathan:22,"_ng":21,sort:[15,40,10,43,25],mulredc:17,cofdec:17,isal:23,qunit:43,acb:36,trait:[40,25],withhilb:41,trail:25,xcasrc:24,sage_trac:[20,32],long_with_underscore_314159:0,cputim:[34,25,15,2,20,18,41,19,9,42,43,39,24],chdir:[15,40,35,7,43],hessian:41,alia:[40,43],alic:20,oct:[15,35,32,0],"2xy5":25,obvious:15,thin:0,freedom:0,meet:15,fetch:41,zsolv:30,control:[0,15,1,38,5,20,21],distrubut:20,setverbos:15,process:[34,32,2,16,17,39,40,19,8,9,10,11,23,41],fsolv:[18,24],high:[31,35,43],tab:[13,25,0,15,3,18,41,20,9,43,39,24],xmin:[4,43,24],onlin:[],tan:24,giusepp:33,dnorm:40,everywher:0,surfac:4,gcd:[43,25,15,1,2,41,19,21,39,24],is_str:[9,2,41,39],six:0,georg:0,sig:15,subdirectori:39,instead:[14,0,15,1,17,18,40,25,7,20,9,43,44],narg:18,nipt:27,sin:[18,27,1,39,4,7,33,43,44,24],chri:0,circular:44,next_prim:[34,17],blackbox:10,overridden:2,singular:[],differenti:[27,43,32],interpet:[15,40,41,31,9,39],"______________________________________________________":20,semisimpl:3,notebook:[40,19,11,22,44,24],parameter_valu:27,rmtree:27,"36x8y4":41,ctl:32,trigonometr:27,"2x2":41,kelli:10,qepcad_bann:0,gapdoc:9,seriou:15,allok:12,stein:[1,2,3,7,9,10,11,14,15,18,21,24,25,31,32,42,35,38,39,40,41,33,43,44],correspond:[12,13,25,0,15,1,27,41,20,9,43,44],element:[21,25,0,40,15,1,2,38,20,39,27,29,41,19,5,9,10,11,44,24,43],issu:[],jmoldata:22,jussieu:20,fastest:17,pellips:0,solv:[32,1,7,36,43,24],move:[1,36,41,0,19],save_imag:7,all_but_finitely_mani:0,sagefunct:19,comma:[15,38,28,43],f_prime:44,avaibl:24,perfect:34,outer:0,ext2:21,ext1:21,x_sols_from_dict:10,expect_upto:23,total:15,pixel:22,crash:11,fourth:0,nonneg:0,handl:[13,27,1,3,10,11],nvar:27,dai:38,newman:17,monomialord:25,sonata:9,nval:15,new_from:25,multiprocess:9,dirac:1,trac:[12,32,9,40,15,1,23,27,41,19,20,44],anyth:[15,1,38,18,41,5,24,7],edit:[2,11,7],targetfil:22,nfi:9,nameerror:[41,19],februari:[5,20],mode:[0,1,17,10,44,24],truth:0,gcdex:43,monomials:25,tracer:[],subset:[15,40,0],sage_extcod:[15,6,39],weyl:3,tangentcon:25,illu:16,panaxiom:[5,38],"_gap_":9,optimal_solv:36,exactly_k:0,"static":[20,22],d_proj_factor:0,frac:7,patch:41,special:[],out:[34,38,32,0,15,8,27,20,5,9,21],variabl:[],user_dir:11,matrix:[43,25,15,1,2,3,41,30,31,32,35],garcia:33,rwth:20,rep:[40,43],cwi:[36,3],suitabl:[25,41,28],rel:[27,36,43,17,30],lattic:40,rec:9,diksolv:36,math:[25,0,26,15,18,36,7,20,9,24],chartabl:20,reduce_load_singular:41,insid:[27,40,0],coef:3,katsura:15,frank:20,ecm:[17,7],manipul:[0,1,38,40,43,44],epsrel:2,solution_dict:10,hankel:32,terminate_async:23,dictionari:[0,17,40,7,10,41],usual:[25,0,26,17,40,7,10,24],releas:[20,24,19],region:0,quo:15,log:[34,43,32,15,39,27,41,21,44],waterloo:18,library_nam:40,could:15,ask:[15,1,44,0],mac:40,keep:[11,36],length:[40,39,17,41,3],outsid:0,geometri:0,testsi:10,localdomain:17,softwar:[12,13,32,27,3,40,31,9,42,33],isbn:40,magma_vers:15,christoph:0,liefunct:3,scene:6,"_sage_var_i":44,echo:[9,23,25],date:[31,35,32,19],sacr:20,mtcar:40,facil:17,"_sage_var_z":44,mkdtemp:[27,40],prioriti:17,"long":[],seq:[18,40],finitefield:21,unknown:[18,9,7,34],licens:[27,38,40,19,5,42,43,24],system:[0,1,2,3,31,7,9,10,11,13,32,15,18,20,21,24,25,5,38,40,41,42,43,44],messag:[25,11,22,41,8],attach:15,encarnacion:0,export_jmol:22,termin:[34,23,11],licenc:40,mwrank_class:28,desired_relative_error:43,"final":[12,20,27,7,0],trigreduc:1,shell:[15,23,38,17,5,9],zxxx:44,with_packag:18,groebner:[],exactli:[31,9,28,41,0],udo:20,horvath:20,cyl:40,gap_gener:[9,20],issb:41,integralclosur:25,emac:8,structur:[0,15,2,17,3,4,40,6,31,10,22],charact:[32,40,15,1,38,17,5,7,31,9,11,39,41],check_output:[9,22],f19:[18,24],xlabel:4,sage32:21,urang:43,sage30:21,reduce_load:[9,7,41],factorintegerecm:7,viewer:[40,7],cohen:[41,3],usyd:15,tide:[],eqn:[1,43,7],mpir:17,have:[0,1,2,7,9,32,15,17,18,19,20,35,22,24,25,26,28,30,31,34,21,40,41,42,43],reserv:[18,9,42],need:[35,32,0,27,1,2,17,20,39,18,40,41,19,31,9,21,22,44,24],turn:[40,28,0],kashdocument:21,alexander_du:12,heft:25,min:[40,43,24],diverg:[43,44],contact:21,roun:[12,30],redefin:[20,41],verboseproc:18,which:[],subject:44,mit:[1,43,44],singl:[0,15,17,40,41,20],uppercas:[5,38],analysi:40,textur:6,unless:[2,6,41,9,11,28],allow:[13,43,0,2,41,19,11,24],quantifi:0,who:[31,35,0],gpfunction:39,jdata:22,eight:0,noredefin:41,"class":[],homogen:[15,41],prove:17,laurent:[17,3],url:0,request:[44,0,26],kaiserslautern:41,face:12,polygamma:18,univari:[12,15,25,41],determin:[43,27,1,6,7,21,41],math_bessel_k:7,validate_mwrank_input:28,fact:2,"_root_1":0,"60d":17,"_root_2":0,text:[34,0,3,6,11,22,44],syntaxerror:31,verbos:[0,3,4,6,8,9,10,11,32,15,17,18,28,36,30,34,38,40,24,41,42,43],magma_gb_standard_opt:15,"365260051l":2,derivedsubgroup:20,withmult:41,trivial:[7,0],write_single_row:30,has_coerce_map_from_impl:41,redirect:17,locat:21,fuer:20,hadn:26,gapfunctionel:9,jar:[9,22,41],forev:32,write_matrix:30,baser:41,smallest:17,suppos:0,barrio:27,local:[43,0,15,19,20,39,40,7,8,9,11,44],devnul:6,cube:[],contribut:[38,0],pull:[13,2],familiar:0,simplest:40,autom:27,increas:39,"_root_k":0,lossless:6,"_root_n":0,enabl:[15,17,3,35,39,24],twice:[41,0],rint:40,trigexpand:1,base2:17,stuff:[2,11,17],integr:[],partit:[18,3],contain:[43,0,15,1,38,17,27,41,9,10,21,22,44],kash_vers:21,view:[0,1,38,40,5,9,39],modulo:[1,9],charpoli:1,x11:40,transcendent:41,rationalfunctionfield:21,popen2:14,gpelement:[39,8],temporarili:9,stack:0,xxxxx:[1,44],modulu:15,gmail:[21,45],asynchron:23,statu:[15,26],correctli:[15,20,21,41,44],sage_loc:[24,0],jmichel:20,tend:27,sqrredc:17,written:[12,36,0,3,18,6,45,30,9,10,43,22,24],proof:[15,17],"164m":17,neither:17,patholog:7,gap_startup:9,bash:13,inputform:7,tempfil:[27,40],job:[20,8],entir:7,"2pi":7,nonfac:12,addit:[13,25,15,2,17,44],get_last_param:17,sage_structured_str_list:41,aqua:40,equal:[12,0,15,1,41,22,44],sol_dict:10,etc:[13,43,0,15,41,19,9,10,11],symmetri:14,instanc:[13,0,15,38,18,19,9,42,43,22,44],equat:[43,32,0,27,1,7,21],triva:16,gp_consol:39,ishomog:41,comment:[9,41],unimpl:44,sol_filt:10,scilab_vers:31,x_c:21,luebeck:20,hyphen:0,frozenset:0,milnor:41,is_prim:17,ucf:36,johann:20,"_start":[18,32,24],polynomialalgebra:21,keitel:16,respect:[43,24],reduce_load_r:40,hebisch:38,quit:[],allow_semicolon:41,isdomain:20,pin:34,gapelement_gener:[9,20],addition:45,"___________________________________________":31,trademark:18,quiz:16,compon:[12,27,10,0,3],besid:0,treat:27,"9x2y7":41,tmp_filenam:[2,3,40,29,7,9,22],liska:0,mike:[5,40,42,30,3],nickel:20,end_si:10,pid:[34,23,16,8,11,2,24],default64:9,degreeoper:20,true_decom:12,x_2:9,togeth:[20,40],panaxiomfunctionel:[5,38],x_1:[9,43],present:[25,7],statist:[40,0],determinist:17,multi:24,matdet:39,primetest:17,set_series_precis:39,defin:[0,1,2,3,7,8,9,11,15,18,20,21,24,25,30,5,38,39,40,41,33,43,44],mixed_volum:10,frac1:43,"__floordiv__":25,auto:17,observ:15,init_cod:[1,38,19,5,9,11],matlab_vers:35,write_arrai:30,helper:[44,0],almost:0,irreduc:[12,18,24],"__reduce__":[1,43],getwd:40,reduce_load_magma:15,archiv:22,sr_integr:44,dual:12,scilabel:31,pcombo:0,avg:[31,35,32],complexfield:10,schilli:40,dietz:36,mutat:21,welcom:[40,33],juan:33,sat_bd:28,defun:33,sqrt:[43,27,1,38,18,40,7,5,21,44,24],member:[9,2,0],python:[12,35,25,0,40,15,38,20,3,18,5,41,19,31,9,21,44,24],nusum:1,pauli:21,reduce_load_gp:39,inc:[18,35],difficult:1,incorrect:1,phi:15,http:[0,1,7,9,36,12,32,15,16,17,18,20,24,25,27,30,5,38,40,41,43,44,45],context:[15,11,41],"9999999999999998e":27,phc:[],r_version:40,logfil:[0,1,3,31,7,9,11,32,15,18,19,21,24,25,5,33,35,38,40,41,42,39],pdf:1,iscm:41,php:17,isci:41,expand:1,off:[0,38,40,5,39,28],center:[0,3],keyboardinterrupt:20,tmpdir:[34,40],well:[26,1,38,3,18,41,5,10,43,44,24],devconf99:7,exampl:[],command:[0,1,3,31,6,7,9,11,13,32,15,17,18,19,20,21,24,25,28,30,5,33,34,35,38,39,40,41,42,43,44],setq:33,setr:41,choos:[41,0],undefin:32,subgroup:20,filedr:27,tlimit:1,find_factor:17,less:[1,21,13,9],fibonacci:18,reduce_load_maxima_funct:1,rand_color:10,obtain:[],invariantquadraticform:2,quit_str:23,sage_polystr:[9,25,41],paul:17,simultan:[24,26],systemat:[15,0],verscheld:10,rekha:14,expon:[2,11,41,7,3],amd64:39,sage7:41,bell:18,sage1:21,sage0:[20,26,21,19],sage3:2,sage2:21,script:[18,22,39,24],add:[0,27,7,31,21,41],foobar:40,lookup:41,gftabl:41,gmp:[9,17,39],match:[10,23,41],sage0_consol:19,cent_root:3,piec:[15,9,21,25,41],five:[28,0],know:[1,26,7,9],press:[32,0,2,38,18,5,24],giacel:24,"2nd":43,recurs:40,panaxiomexpectfunct:[5,38],"000d":31,mupadfunctionel:42,success:[15,21],"000e":41,betainc:32,fricasfunctionel:5,exact2:0,necessari:[31,10,35,32],martin:[20,41],page:[13,6,38],revers:[15,25,41],"05publicacion":27,recfield:20,yqiang:45,decor:[15,41,8],quartz:40,"export":7,is_gpel:39,flush:[15,41],proper:34,guarante:17,is_nam:[1,2,3,31,7,9,11,32,15,18,19,20,21,24,25,26,5,33,35,38,39,40,41,42,43,44],sage2matlab_matrix_str:35,librari:[],tmp:[40,30],tmpfr_set_str:27,lead:[15,1,43,25,44],rstr:40,leak:15,avoid:[0,8,10,22,44,24],slide:0,overlap:[7,0],meier:20,frankjankowski:16,estim:[43,17],leav:[5,38],digiteo:31,perm_gp:9,symbol:[25,0,27,1,38,40,7,43,44,24,41],preload:17,tmin:43,importerror:40,imaginari:[10,21,43],usag:[15,17,6,41,11,45],n_comp:3,although:[41,0],gap_consol:9,"11x":7,stage:17,about:[13,39,0,34,15,1,17,3,18,40,31,10,21,44,24],actual:[13,32,34,23,17,40,41,19,9,39],python_to_ecl:44,echelon_form:1,column:[37,32,30],"2xy4":25,"2xy3":25,ander:14,constructor:[15,25,41,0],fals:[0,1,2,3,5,6,7,8,9,10,11,32,15,17,18,19,20,21,22,24,25,26,30,31,33,34,35,36,38,39,40,41,42,43,44],number_of_children:0,disabl:[11,17,41],syntax_error:6,own:[15,9,19,40,3],primal:[17,41],mrat:44,automat:[21,0,43,15,38,40,41,5,11,39,28],dataset:40,warranti:40,phcpack:10,empti:[34,6,25,0],magmafunctionel:15,pitfal:[],forget:[11,44],decom0:12,decom1:12,gnuplot_out_fil:43,van:3,irredund:12,val:[43,17,41],stanli:0,rotat:4,appl:32,combined_matrix:[31,35],inner:0,"var":[0,1,2,3,7,9,32,15,18,19,35,24,25,26,27,31,33,21,38,39,40,41,42,43,44],individu:[11,14,0],"function":[],mupad_consol:42,isfinit:20,histogram:40,sage_tmp:[15,9,22,40],bui:7,npar:27,bug:[12,25,26,1,17,40,41,20,43,44],decomp:15,mpzmod:17,count:10,made:[27,25,41,30,44],seriesprecis:39,temp:17,whether:[21,25,0,15,2,17,39,41,9,10,11,44],displai:[18,1,23,38,4,40,6,7,30,8,5,9,43,22,24,28],troubl:7,column_vector2:[31,35],record:[9,20],below:[13,25,0,15,17,3,40,41,20,21,44],column_vector1:[31,35],limit:[15,1,44,37],indefinit:[43,24],testfil:22,octaveel:32,otherwis:[0,15,17,43,44,24],problem:[0,15,1,17,27,41,43],verbose_start:[9,11],evalu:[0,1,3,31,7,9,11,32,15,18,19,20,21,24,25,27,5,35,37,38,39,40,41,43,44],"int":[27,3,4,40,41,43,39,24],dure:[34,25,0,38,41,21],indata:29,inp:17,"4040k":17,append_:21,operand:27,implement:[13,14,0,27,1,2,38,17,32,40,36,30,20,10,43,44],evalf:24,our:[18,41,24,0,19],ind:40,inf:[1,17,40],eric:36,probabl:[15,43,17],detail:[32,15,17,40,33,7,30,9,10,44,24,41],virtual:22,arctan:[27,44],other:[],bool:[21,43,15,2,20,39,40,6,8,9,33,11,22,44],futur:[15,18],rememb:[31,35,32,0],plot_paths_2d:10,set_default:39,basic1:7,singularel:41,get_record_el:9,stat:40,repeat:[15,27,40],potenti:7,gcc:[9,39,20],previous:41,involut:15,singularerror:41,nrow:[41,30],scientif:31,arjeh:3,bca:36,prpno:17,qsolv:30,"_sage_repr":7,isprincip:[15,21],partli:0,invari:[1,38,44,43],sebast:21,get_se:2},objtypes:{"0":"py:module","1":"py:method","2":"py:class","3":"py:function","4":"py:exception"},objnames:{"0":["py","module","Python module"],"1":["py","method","Python method"],"2":["py","class","Python class"],"3":["py","function","Python function"],"4":["py","exception","Python exception"]},filenames:["sage/interfaces/qepcad","sage/interfaces/maxima","sage/interfaces/interface","sage/interfaces/lie","sage/interfaces/gnuplot","sage/interfaces/fricas","sage/interfaces/tachyon","sage/interfaces/mathematica","sage/interfaces/quit","sage/interfaces/gap","sage/interfaces/phc","sage/interfaces/expect","sage/interfaces/frobby","index","sage/interfaces/gfan","sage/interfaces/magma","sage/interfaces/cleaner","sage/interfaces/ecm","sage/interfaces/maple","sage/interfaces/sage0","sage/interfaces/gap3","sage/interfaces/kash","sage/interfaces/jmoldata","sage/interfaces/sagespawn","sage/interfaces/giac","sage/interfaces/macaulay2","sage/interfaces/psage","sage/interfaces/tides","sage/interfaces/mwrank","sage/interfaces/read_data","sage/interfaces/four_ti_2","sage/interfaces/scilab","sage/interfaces/octave","sage/interfaces/lisp","sage/interfaces/qsieve","sage/interfaces/matlab","sage/interfaces/rubik","sage/interfaces/magma_free","sage/interfaces/axiom","sage/interfaces/gp","sage/interfaces/r","sage/interfaces/singular","sage/interfaces/mupad","sage/interfaces/maxima_abstract","sage/interfaces/maxima_lib","sage/interfaces/povray"],titles:["Interface to QEPCAD","Pexpect interface to Maxima","Common Interface Functionality","Interface to LiE","Interface to the Gnuplot interpreter","Interface to FriCAS","The Tachyon Ray Tracer","Interface to Mathematica","Quitting interfaces","Interface to GAP","Interface to PHC.","Common Interface Functionality through Pexpect","Interface to Frobby for fast computations on monomial ideals.","Interpreter Interfaces","Interface to Groebner Fan","Interface to Magma","Interface to the Sage cleaner","The Elliptic Curve Factorization Method","Interface to Maple","Interface to Sage","Interface to GAP3","Interface to KASH","Interface for extracting data and generating images from Jmol readable files.","Sage wrapper around pexpect’s <tt class=\"docutils literal\"><span class=\"pre\">spawn</span></tt> class","Interface to Giac","Interface to Macaulay2","Parallel Interface to the Sage interpreter","Interface to TIDES","Interface to mwrank","An interface to read data files","Interface to 4ti2","Interface to Scilab","Interface to GNU Octave","Lisp Interface","Interface to Bill Hart’s Quadratic Sieve","Interface to MATLAB","Interface to several Rubik’s cube solvers.","Interface to the free online MAGMA calculator","Interface to Axiom","Interface to the GP calculator of PARI/GP","Interface to R","Interface to Singular","Interface to MuPAD","Abstract interface to Maxima","Library interface to Maxima","POV-Ray, The Persistence of Vision Ray Tracer"],objects:{"sage.interfaces.fricas.FriCAS":{console:[5,1,1,""]},"sage.interfaces.rubik.OptimalSolver":{ready:[36,1,1,""],start:[36,1,1,""],stop:[36,1,1,""],solve:[36,1,1,""],format_cube:[36,1,1,""]},"sage.interfaces.qepcad":{QepcadFunction:[0,2,1,""],Qepcad_expect:[0,2,1,""],qepcad_formula_factory:[0,2,1,""],Qepcad:[0,2,1,""],qepcad_console:[0,3,1,""],QepcadCell:[0,2,1,""],qepcad_version:[0,3,1,""],qepcad:[0,3,1,""],qformula:[0,2,1,""],qepcad_banner:[0,3,1,""]},"sage.interfaces.maxima_abstract":{MaximaAbstract:[43,2,1,""],maxima_console:[43,3,1,""],MaximaAbstractElementFunction:[43,2,1,""],maxima_version:[43,3,1,""],MaximaAbstractFunctionElement:[43,2,1,""],MaximaAbstractFunction:[43,2,1,""],MaximaAbstractElement:[43,2,1,""],reduce_load_MaximaAbstract_function:[43,3,1,""]},"sage.interfaces.scilab":{ScilabElement:[31,2,1,""],Scilab:[31,2,1,""],scilab_console:[31,3,1,""],scilab_version:[31,3,1,""]},"sage.interfaces.lie.LiE":{get_using_file:[3,1,1,""],set:[3,1,1,""],console:[3,1,1,""],help:[3,1,1,""],get:[3,1,1,""],read:[3,1,1,""],function_call:[3,1,1,""],trait_names:[3,1,1,""],version:[3,1,1,""],eval:[3,1,1,""]},"sage.interfaces.mathematica.MathematicaElement":{show:[7,1,1,""],save_image:[7,1,1,""],str:[7,1,1,""],N:[7,1,1,""]},"sage.interfaces.sagespawn.SageSpawn":{close:[23,1,1,""],terminate_async:[23,1,1,""],expect_peek:[23,1,1,""],expect_upto:[23,1,1,""]},"sage.interfaces.interface.InterfaceFunctionElement":{help:[2,1,1,""]},"sage.interfaces.kash.Kash":{help_search:[21,1,1,""],console:[21,1,1,""],help:[21,1,1,""],get:[21,1,1,""],version:[21,1,1,""],eval:[21,1,1,""],set:[21,1,1,""]},"sage.interfaces.maxima_lib.MaximaLib":{sr_sum:[44,1,1,""],set:[44,1,1,""],sr_integral:[44,1,1,""],get:[44,1,1,""],lisp:[44,1,1,""],clear:[44,1,1,""],eval:[44,1,1,""],sr_limit:[44,1,1,""],sr_tlimit:[44,1,1,""]},"sage.interfaces.gap.GapElement_generic":{is_string:[9,1,1,""],bool:[9,1,1,""]},"sage.interfaces.axiom.Axiom":{console:[38,1,1,""]},"sage.interfaces.qsieve":{qsieve:[34,3,1,""],qsieve_block:[34,3,1,""],data_to_list:[34,3,1,""],tmpdir:[34,3,1,""],qsieve_nonblock:[34,2,1,""]},"sage.interfaces.mupad":{MupadFunction:[42,2,1,""],reduce_load_mupad:[42,3,1,""],mupad_console:[42,3,1,""],MupadFunctionElement:[42,2,1,""],Mupad:[42,2,1,""],MupadElement:[42,2,1,""]},"sage.interfaces.mwrank":{Mwrank_class:[28,2,1,""],Mwrank:[28,3,1,""],mwrank_console:[28,3,1,""],validate_mwrank_input:[28,3,1,""]},"sage.interfaces.gap3.GAP3Record":{operations:[20,1,1,""],recfields:[20,1,1,""],trait_names:[20,1,1,""]},"sage.interfaces.cleaner":{cleaner:[16,3,1,""],start_cleaner:[16,3,1,""]},"sage.interfaces.gp":{Gp:[39,2,1,""],GpElement:[39,2,1,""],gp_version:[39,3,1,""],is_GpElement:[39,3,1,""],reduce_load_GP:[39,3,1,""],gp_console:[39,3,1,""],GpFunctionElement:[39,2,1,""],GpFunction:[39,2,1,""]},"sage.interfaces.tachyon":{TachyonRT:[6,2,1,""]},"sage.interfaces.qepcad.QepcadCell":{index:[0,1,1,""],number_of_children:[0,1,1,""],level:[0,1,1,""],sample_point:[0,1,1,""],sample_point_dict:[0,1,1,""],signs:[0,1,1,""],set_truth:[0,1,1,""]},"sage.interfaces.matlab":{reduce_load_Matlab:[35,3,1,""],matlab_version:[35,3,1,""],MatlabElement:[35,2,1,""],Matlab:[35,2,1,""],matlab_console:[35,3,1,""]},"sage.interfaces.maxima_abstract.MaximaAbstractElement":{real:[43,1,1,""],derivative:[43,1,1,""],partial_fraction_decomposition:[43,1,1,""],numer:[43,1,1,""],imag:[43,1,1,""],integral:[43,1,1,""],trait_names:[43,1,1,""],subst:[43,1,1,""],comma:[43,1,1,""],str:[43,1,1,""],nintegral:[43,1,1,""],integrate:[43,1,1,""],diff:[43,1,1,""],bool:[43,1,1,""],dot:[43,1,1,""]},"sage.interfaces.read_data":{read_data:[29,3,1,""]},"sage.interfaces.gnuplot":{gnuplot_console:[4,3,1,""],Gnuplot:[4,2,1,""]},"sage.interfaces.mathematica":{MathematicaFunctionElement:[7,2,1,""],Mathematica:[7,2,1,""],clean_output:[7,3,1,""],mathematica_console:[7,3,1,""],MathematicaElement:[7,2,1,""],MathematicaFunction:[7,2,1,""],reduce_load:[7,3,1,""]},"sage.interfaces.mathematica.Mathematica":{chdir:[7,1,1,""],console:[7,1,1,""],help:[7,1,1,""],get:[7,1,1,""],trait_names:[7,1,1,""],set:[7,1,1,""],eval:[7,1,1,""]},"sage.interfaces.scilab.ScilabElement":{set:[31,1,1,""]},"sage.interfaces.sage0.Sage":{set:[19,1,1,""],console:[19,1,1,""],get:[19,1,1,""],preparse:[19,1,1,""],clear:[19,1,1,""],cputime:[19,1,1,""],trait_names:[19,1,1,""],version:[19,1,1,""],eval:[19,1,1,""],"new":[19,1,1,""]},"sage.interfaces.mwrank.Mwrank_class":{console:[28,1,1,""],eval:[28,1,1,""]},"sage.interfaces.gp.GpElement":{is_string:[39,1,1,""],trait_names:[39,1,1,""],bool:[39,1,1,""]},"sage.interfaces.ecm":{ECM:[17,2,1,""]},"sage.interfaces.giac.GiacElement":{unapply:[24,1,1,""],integrate:[24,1,1,""],sum:[24,1,1,""],integral:[24,1,1,""],trait_names:[24,1,1,""]},"sage.interfaces.jmoldata":{JmolData:[22,2,1,""]},"sage.interfaces.gap.Gap_generic":{unbind:[9,1,1,""],function_call:[9,1,1,""],get_record_element:[9,1,1,""],load_package:[9,1,1,""],trait_names:[9,1,1,""],version:[9,1,1,""],eval:[9,1,1,""],interrupt:[9,1,1,""]},"sage.interfaces.maple.Maple":{load:[18,1,1,""],set:[18,1,1,""],console:[18,1,1,""],help:[18,1,1,""],completions:[18,1,1,""],get:[18,1,1,""],clear:[18,1,1,""],cputime:[18,1,1,""],source:[18,1,1,""],trait_names:[18,1,1,""],expect:[18,1,1,""],with_package:[18,1,1,""]},"sage.interfaces.maxima.MaximaElement":{display2d:[1,1,1,""]},"sage.interfaces.r.RElement":{trait_names:[40,1,1,""],stat_model:[40,1,1,""],dot_product:[40,1,1,""],tilde:[40,1,1,""]},"sage.interfaces.psage":{PSageElement:[26,2,1,""],PSage:[26,2,1,""]},"sage.interfaces.magma_free.MagmaFree":{eval:[37,1,1,""]},"sage.interfaces.gap.Gap":{save_workspace:[9,1,1,""],console:[9,1,1,""],help:[9,1,1,""],get:[9,1,1,""],cputime:[9,1,1,""],trait_names:[9,1,1,""],set:[9,1,1,""],set_seed:[9,1,1,""]},"sage.interfaces.mupad.MupadElement":{trait_names:[42,1,1,""]},"sage.interfaces.povray":{POVRay:[45,2,1,""]},"sage.interfaces.giac":{GiacFunction:[24,2,1,""],giac_console:[24,3,1,""],GiacElement:[24,2,1,""],reduce_load_Giac:[24,3,1,""],Giac:[24,2,1,""],GiacFunctionElement:[24,2,1,""]},"sage.interfaces.maxima_abstract.MaximaAbstract":{"function":[43,1,1,""],version:[43,1,1,""],unit_quadratic_integer:[43,1,1,""],console:[43,1,1,""],de_solve:[43,1,1,""],completions:[43,1,1,""],demo:[43,1,1,""],describe:[43,1,1,""],help:[43,1,1,""],trait_names:[43,1,1,""],cputime:[43,1,1,""],plot_list:[43,1,1,""],de_solve_laplace:[43,1,1,""],chdir:[43,1,1,""],plot2d:[43,1,1,""],plot3d:[43,1,1,""],plot2d_parametric:[43,1,1,""],plot3d_parametric:[43,1,1,""],solve_linear:[43,1,1,""],example:[43,1,1,""],plot_multilist:[43,1,1,""]},"sage.interfaces.axiom":{axiom_console:[38,3,1,""],AxiomExpectFunction:[38,2,1,""],is_AxiomElement:[38,3,1,""],PanAxiom:[38,2,1,""],AxiomElement:[38,2,1,""],PanAxiomFunctionElement:[38,2,1,""],reduce_load_Axiom:[38,3,1,""],PanAxiomExpectFunction:[38,2,1,""],PanAxiomElement:[38,2,1,""],AxiomFunctionElement:[38,2,1,""],Axiom:[38,2,1,""]},"sage.interfaces.rubik.DikSolver":{format_cube:[36,1,1,""],solve:[36,1,1,""]},"sage.interfaces.lie":{LiE:[3,2,1,""],LiEFunction:[3,2,1,""],LiEElement:[3,2,1,""],LiEFunctionElement:[3,2,1,""],reduce_load_lie:[3,3,1,""],is_LiEElement:[3,3,1,""],lie_console:[3,3,1,""],lie_version:[3,3,1,""]},"sage.interfaces.macaulay2.Macaulay2Element":{to_sage:[25,1,1,""],external_string:[25,1,1,""],subs:[25,1,1,""],trait_names:[25,1,1,""],starstar:[25,1,1,""],repr:[25,1,1,""],structure_sheaf:[25,1,1,""],substitute:[25,1,1,""],underscore:[25,1,1,""],sharp:[25,1,1,""],sage_polystring:[25,1,1,""],dot:[25,1,1,""],cls:[25,1,1,""]},"sage.interfaces.gap3":{gap3_console:[20,3,1,""],gap3_version:[20,3,1,""],Gap3:[20,2,1,""],GAP3Element:[20,2,1,""],GAP3Record:[20,2,1,""]},"sage.interfaces.axiom.PanAxiom":{trait_names:[38,1,1,""],set:[38,1,1,""],get:[38,1,1,""]},"sage.interfaces.psage.PSageElement":{is_locked:[26,1,1,""]},"sage.interfaces.povray.POVRay":{usage:[45,1,1,""]},"sage.interfaces.jmoldata.JmolData":{export_image:[22,1,1,""],is_jvm_available:[22,1,1,""]},"sage.interfaces.mupad.MupadFunctionElement":{trait_names:[42,1,1,""]},"sage.interfaces.maxima_lib.MaximaLibElement":{display2d:[44,1,1,""],ecl:[44,1,1,""],to_poly_solve:[44,1,1,""]},"sage.interfaces.singular.SingularGBLogPrettyPrinter":{write:[41,1,1,""],flush:[41,1,1,""]},"sage.interfaces.phc":{PHC:[10,2,1,""],PHC_Object:[10,2,1,""],get_variable_list:[10,3,1,""],get_solution_dicts:[10,3,1,""],get_classified_solution_dicts:[10,3,1,""]},"sage.interfaces.tides":{genfiles_mpfr:[27,3,1,""],subexpressions_list:[27,3,1,""],genfiles_mintides:[27,3,1,""],remove_repeated:[27,3,1,""],remove_constants:[27,3,1,""]},"sage.interfaces.frobby.Frobby":{associated_primes:[12,1,1,""],hilbert:[12,1,1,""],irreducible_decomposition:[12,1,1,""],dimension:[12,1,1,""],alexander_dual:[12,1,1,""]},"sage.interfaces.maple.MapleElement":{trait_names:[18,1,1,""]},"sage.interfaces.interface.Interface":{get_using_file:[2,1,1,""],execute:[2,1,1,""],set:[2,1,1,""],console:[2,1,1,""],name:[2,1,1,""],get:[2,1,1,""],set_seed:[2,1,1,""],clear:[2,1,1,""],cputime:[2,1,1,""],get_seed:[2,1,1,""],read:[2,1,1,""],call:[2,1,1,""],function_call:[2,1,1,""],eval:[2,1,1,""],"new":[2,1,1,""],rand_seed:[2,1,1,""],interact:[2,1,1,""],help:[2,1,1,""]},"sage.interfaces.r.R":{set:[40,1,1,""],help:[40,1,1,""],completions:[40,1,1,""],library:[40,1,1,""],install_packages:[40,1,1,""],available_packages:[40,1,1,""],plot:[40,1,1,""],console:[40,1,1,""],na:[40,1,1,""],convert_r_list:[40,1,1,""],source:[40,1,1,""],trait_names:[40,1,1,""],version:[40,1,1,""],call:[40,1,1,""],get:[40,1,1,""],read:[40,1,1,""],set_seed:[40,1,1,""],function_call:[40,1,1,""],eval:[40,1,1,""],png:[40,1,1,""],chdir:[40,1,1,""],require:[40,1,1,""]},"sage.interfaces.phc.PHC_Object":{save_as_start:[10,1,1,""],variable_list:[10,1,1,""],solutions:[10,1,1,""],classified_solution_dicts:[10,1,1,""],solution_dicts:[10,1,1,""]},"sage.interfaces.maxima":{reduce_load_Maxima_function:[1,3,1,""],MaximaFunction:[1,2,1,""],MaximaElementFunction:[1,2,1,""],MaximaElement:[1,2,1,""],is_MaximaElement:[1,3,1,""],reduce_load_Maxima:[1,3,1,""],MaximaFunctionElement:[1,2,1,""],Maxima:[1,2,1,""]},"sage.interfaces.lisp":{reduce_load_Lisp:[33,3,1,""],Lisp:[33,2,1,""],LispFunctionElement:[33,2,1,""],LispFunction:[33,2,1,""],is_LispElement:[33,3,1,""],lisp_console:[33,3,1,""],LispElement:[33,2,1,""]},"sage.interfaces.ecm.ECM":{recommended_B1:[17,1,1,""],find_factor:[17,1,1,""],interact:[17,1,1,""],time:[17,1,1,""],factor:[17,1,1,""],one_curve:[17,1,1,""],get_last_params:[17,1,1,""]},"sage.interfaces.qepcad.Qepcad":{set_truth_value:[0,1,1,""],assume:[0,1,1,""],make_cells:[0,1,1,""],solution_extension:[0,1,1,""],final_stats:[0,1,1,""],cell:[0,1,1,""],phase:[0,1,1,""],trait_names:[0,1,1,""],answer:[0,1,1,""]},"sage.interfaces.interface.InterfaceElement":{get_using_file:[2,1,1,""],name:[2,1,1,""],attribute:[2,1,1,""],sage:[2,1,1,""],is_string:[2,1,1,""],bool:[2,1,1,""],gen:[2,1,1,""],hasattr:[2,1,1,""]},"sage.interfaces.magma":{magma_console:[15,3,1,""],extcode_dir:[15,3,1,""],MagmaGBLogPrettyPrinter:[15,2,1,""],MagmaGBDefaultContext:[15,2,1,""],is_MagmaElement:[15,3,1,""],MagmaElement:[15,2,1,""],Magma:[15,2,1,""],magma_gb_standard_options:[15,3,1,""],reduce_load_Magma:[15,3,1,""],magma_version:[15,3,1,""],MagmaFunctionElement:[15,2,1,""],MagmaFunction:[15,2,1,""]},"sage.interfaces.lisp.Lisp":{set:[33,1,1,""],console:[33,1,1,""],help:[33,1,1,""],get:[33,1,1,""],function_call:[33,1,1,""],trait_names:[33,1,1,""],version:[33,1,1,""],kill:[33,1,1,""],eval:[33,1,1,""]},"sage.interfaces.magma.Magma":{load:[15,1,1,""],set:[15,1,1,""],help:[15,1,1,""],SetVerbose:[15,1,1,""],function_call:[15,1,1,""],Attach:[15,1,1,""],attach_spec:[15,1,1,""],console:[15,1,1,""],attach:[15,1,1,""],get_verbose:[15,1,1,""],ideal:[15,1,1,""],AttachSpec:[15,1,1,""],objgens:[15,1,1,""],trait_names:[15,1,1,""],version:[15,1,1,""],get:[15,1,1,""],cputime:[15,1,1,""],set_seed:[15,1,1,""],bar_call:[15,1,1,""],eval:[15,1,1,""],set_verbose:[15,1,1,""],chdir:[15,1,1,""],clear:[15,1,1,""],GetVerbose:[15,1,1,""]},"sage.interfaces.singular.SingularElement":{set_ring:[41,1,1,""],sage_flattened_str_list:[41,1,1,""],sage_structured_str_list:[41,1,1,""],sage_matrix:[41,1,1,""],is_string:[41,1,1,""],trait_names:[41,1,1,""],sage_poly:[41,1,1,""],sage_global_ring:[41,1,1,""],sage_polystring:[41,1,1,""],attrib:[41,1,1,""],type:[41,1,1,""]},"sage.interfaces.maxima_lib":{sage_rat:[44,3,1,""],is_MaximaLibElement:[44,3,1,""],max_to_sr:[44,3,1,""],MaximaLibElementFunction:[44,2,1,""],MaximaLibFunctionElement:[44,2,1,""],parse_max_string:[44,3,1,""],sr_to_max:[44,3,1,""],mlist_to_sage:[44,3,1,""],mdiff_to_sage:[44,3,1,""],max_to_string:[44,3,1,""],pyobject_to_max:[44,3,1,""],mrat_to_sage:[44,3,1,""],mqapply_to_sage:[44,3,1,""],MaximaLibFunction:[44,2,1,""],reduce_load_MaximaLib:[44,3,1,""],max_at_to_sage:[44,3,1,""],dummy_integrate:[44,3,1,""],stdout_to_string:[44,3,1,""],MaximaLibElement:[44,2,1,""],MaximaLib:[44,2,1,""]},"sage.interfaces.psage.PSage":{is_locked:[26,1,1,""],set:[26,1,1,""],eval:[26,1,1,""],get:[26,1,1,""]},"sage.interfaces.fricas":{is_FriCASElement:[5,3,1,""],FriCASFunctionElement:[5,2,1,""],FriCAS:[5,2,1,""],fricas_console:[5,3,1,""],FriCASExpectFunction:[5,2,1,""],FriCASElement:[5,2,1,""],reduce_load_fricas:[5,3,1,""]},"sage.interfaces.gnuplot.Gnuplot":{plot:[4,1,1,""],plot3d_parametric:[4,1,1,""],gnuplot:[4,1,1,""],interact:[4,1,1,""],plot3d:[4,1,1,""],console:[4,1,1,""]},"sage.interfaces.octave.Octave":{quit:[32,1,1,""],set:[32,1,1,""],console:[32,1,1,""],get:[32,1,1,""],clear:[32,1,1,""],sage2octave_matrix_string:[32,1,1,""],version:[32,1,1,""],set_seed:[32,1,1,""],solve_linear_system:[32,1,1,""],de_system_plot:[32,1,1,""]},"sage.interfaces.maxima.Maxima":{lisp:[1,1,1,""],clear:[1,1,1,""],set:[1,1,1,""],set_seed:[1,1,1,""],get:[1,1,1,""]},"sage.interfaces.four_ti_2.FourTi2":{zsolve:[30,1,1,""],read_matrix:[30,1,1,""],graver:[30,1,1,""],call:[30,1,1,""],circuits:[30,1,1,""],groebner:[30,1,1,""],write_single_row:[30,1,1,""],ppi:[30,1,1,""],write_matrix:[30,1,1,""],minimize:[30,1,1,""],rays:[30,1,1,""],write_array:[30,1,1,""],directory:[30,1,1,""],temp_project:[30,1,1,""],qsolve:[30,1,1,""],hilbert:[30,1,1,""]},"sage.interfaces.quit":{is_running:[8,3,1,""],invalidate_all:[8,3,1,""],expect_quitall:[8,3,1,""],kill_spawned_jobs:[8,3,1,""]},"sage.interfaces.magma.MagmaElement":{sub:[15,1,1,""],gen_names:[15,1,1,""],trait_names:[15,1,1,""],set_magma_attribute:[15,1,1,""],evaluate:[15,1,1,""],get_magma_attribute:[15,1,1,""],gens:[15,1,1,""],assign_names:[15,1,1,""],ideal:[15,1,1,""],list_attributes:[15,1,1,""],eval:[15,1,1,""],AssignNames:[15,1,1,""],gen:[15,1,1,""],quo:[15,1,1,""],methods:[15,1,1,""]},"sage.interfaces":{cleaner:[16,0,0,"-"],gp:[39,0,0,"-"],ecm:[17,0,0,"-"],tachyon:[6,0,0,"-"],fricas:[5,0,0,"-"],magma:[15,0,0,"-"],four_ti_2:[30,0,0,"-"],expect:[11,0,0,"-"],mupad:[42,0,0,"-"],mwrank:[28,0,0,"-"],psage:[26,0,0,"-"],maple:[18,0,0,"-"],lie:[3,0,0,"-"],gfan:[14,0,0,"-"],gnuplot:[4,0,0,"-"],mathematica:[7,0,0,"-"],sage0:[19,0,0,"-"],frobby:[12,0,0,"-"],matlab:[35,0,0,"-"],rubik:[36,0,0,"-"],povray:[45,0,0,"-"],giac:[24,0,0,"-"],maxima_abstract:[43,0,0,"-"],axiom:[38,0,0,"-"],qsieve:[34,0,0,"-"],macaulay2:[25,0,0,"-"],maxima_lib:[44,0,0,"-"],sagespawn:[23,0,0,"-"],singular:[41,0,0,"-"],phc:[10,0,0,"-"],tides:[27,0,0,"-"],quit:[8,0,0,"-"],gap:[9,0,0,"-"],gap3:[20,0,0,"-"],kash:[21,0,0,"-"],octave:[32,0,0,"-"],"interface":[2,0,0,"-"],read_data:[29,0,0,"-"],magma_free:[37,0,0,"-"],lisp:[33,0,0,"-"],r:[40,0,0,"-"],jmoldata:[22,0,0,"-"],qepcad:[0,0,0,"-"],scilab:[31,0,0,"-"],maxima:[1,0,0,"-"]},"sage.interfaces.sage0":{sage0_version:[19,3,1,""],reduce_load_element:[19,3,1,""],Sage:[19,2,1,""],sage0_console:[19,3,1,""],reduce_load_Sage:[19,3,1,""],SageElement:[19,2,1,""],SageFunction:[19,2,1,""]},"sage.interfaces.maxima_abstract.MaximaAbstractElementFunction":{integrate:[43,1,1,""],definition:[43,1,1,""],integral:[43,1,1,""],arguments:[43,1,1,""]},"sage.interfaces.kash":{kash_console:[21,3,1,""],is_KashElement:[21,3,1,""],KashElement:[21,2,1,""],kash_version:[21,3,1,""],Kash:[21,2,1,""],KashDocumentation:[21,2,1,""],reduce_load_Kash:[21,3,1,""]},"sage.interfaces.interface":{InterfaceElement:[2,2,1,""],InterfaceFunction:[2,2,1,""],Interface:[2,2,1,""],is_InterfaceElement:[2,3,1,""],AsciiArtString:[2,2,1,""],InterfaceFunctionElement:[2,2,1,""]},"sage.interfaces.magma_free":{MagmaFree:[37,2,1,""],MagmaExpr:[37,2,1,""],magma_free_eval:[37,3,1,""]},"sage.interfaces.gap3.Gap3":{console:[20,1,1,""],help:[20,1,1,""],cputime:[20,1,1,""]},"sage.interfaces.magma.MagmaGBLogPrettyPrinter":{write:[15,1,1,""],flush:[15,1,1,""]},"sage.interfaces.sagespawn":{SageSpawn:[23,2,1,""]},"sage.interfaces.gp.Gp":{kill:[39,1,1,""],set:[39,1,1,""],get_precision:[39,1,1,""],get_default:[39,1,1,""],get:[39,1,1,""],get_real_precision:[39,1,1,""],set_series_precision:[39,1,1,""],cputime:[39,1,1,""],console:[39,1,1,""],trait_names:[39,1,1,""],version:[39,1,1,""],set_seed:[39,1,1,""],set_default:[39,1,1,""],set_precision:[39,1,1,""],get_series_precision:[39,1,1,""],new_with_bits_prec:[39,1,1,""],set_real_precision:[39,1,1,""],help:[39,1,1,""]},"sage.interfaces.matlab.MatlabElement":{set:[35,1,1,""]},"sage.interfaces.macaulay2.Macaulay2":{use:[25,1,1,""],set:[25,1,1,""],console:[25,1,1,""],help:[25,1,1,""],get:[25,1,1,""],trait_names:[25,1,1,""],cputime:[25,1,1,""],ideal:[25,1,1,""],version:[25,1,1,""],eval:[25,1,1,""],ring:[25,1,1,""],new_from:[25,1,1,""],restart:[25,1,1,""]},"sage.interfaces.singular.Singular":{load:[41,1,1,""],set:[41,1,1,""],LIB:[41,1,1,""],setring:[41,1,1,""],ring:[41,1,1,""],has_coerce_map_from_impl:[41,1,1,""],current_ring:[41,1,1,""],console:[41,1,1,""],matrix:[41,1,1,""],lib:[41,1,1,""],trait_names:[41,1,1,""],ideal:[41,1,1,""],version:[41,1,1,""],current_ring_name:[41,1,1,""],option:[41,1,1,""],get:[41,1,1,""],cputime:[41,1,1,""],set_seed:[41,1,1,""],eval:[41,1,1,""],string:[41,1,1,""],set_ring:[41,1,1,""],clear:[41,1,1,""],list:[41,1,1,""]},"sage.interfaces.r":{RElement:[40,2,1,""],is_RElement:[40,3,1,""],RFunctionElement:[40,2,1,""],r_console:[40,3,1,""],RFunction:[40,2,1,""],r_version:[40,3,1,""],R:[40,2,1,""],HelpExpression:[40,2,1,""],reduce_load_R:[40,3,1,""]},"sage.interfaces.phc.PHC":{plot_paths_2d:[10,1,1,""],start_from:[10,1,1,""],mixed_volume:[10,1,1,""],blackbox:[10,1,1,""],path_track:[10,1,1,""]},"sage.interfaces.qepcad.qepcad_formula_factory":{A:[0,1,1,""],or_:[0,1,1,""],C:[0,1,1,""],implies:[0,1,1,""],exists:[0,1,1,""],G:[0,1,1,""],F:[0,1,1,""],not_:[0,1,1,""],iff:[0,1,1,""],and_:[0,1,1,""],exactly_k:[0,1,1,""],atomic:[0,1,1,""],formula:[0,1,1,""],forall:[0,1,1,""],X:[0,1,1,""],infinitely_many:[0,1,1,""],E:[0,1,1,""],quantifier:[0,1,1,""],connected_subset:[0,1,1,""],all_but_finitely_many:[0,1,1,""]},"sage.interfaces.four_ti_2":{FourTi2:[30,2,1,""]},"sage.interfaces.expect":{is_ExpectElement:[11,3,1,""],ExpectFunction:[11,2,1,""],console:[11,3,1,""],gc_disabled:[11,2,1,""],StdOutContext:[11,2,1,""],Expect:[11,2,1,""],ExpectElement:[11,2,1,""],FunctionElement:[11,2,1,""]},"sage.interfaces.matlab.Matlab":{set:[35,1,1,""],console:[35,1,1,""],get:[35,1,1,""],chdir:[35,1,1,""],whos:[35,1,1,""],version:[35,1,1,""],strip_answer:[35,1,1,""],sage2matlab_matrix_string:[35,1,1,""]},"sage.interfaces.lie.LiEElement":{trait_names:[3,1,1,""],type:[3,1,1,""]},"sage.interfaces.maple":{MapleFunctionElement:[18,2,1,""],maple_console:[18,3,1,""],reduce_load_Maple:[18,3,1,""],MapleFunction:[18,2,1,""],MapleElement:[18,2,1,""],Maple:[18,2,1,""]},"sage.interfaces.lisp.LispElement":{bool:[33,1,1,""]},"sage.interfaces.gap.GapElement":{trait_names:[9,1,1,""],str:[9,1,1,""]},"sage.interfaces.axiom.PanAxiomElement":{as_type:[38,1,1,""],type:[38,1,1,""],comma:[38,1,1,""],unparsed_input_form:[38,1,1,""]},"sage.interfaces.giac.Giac":{set:[24,1,1,""],console:[24,1,1,""],help:[24,1,1,""],completions:[24,1,1,""],get:[24,1,1,""],clear:[24,1,1,""],cputime:[24,1,1,""],trait_names:[24,1,1,""],version:[24,1,1,""],expect:[24,1,1,""],eval:[24,1,1,""]},"sage.interfaces.frobby":{Frobby:[12,2,1,""]},"sage.interfaces.rubik":{OptimalSolver:[36,2,1,""],CubexSolver:[36,2,1,""],DikSolver:[36,2,1,""],SingNot:[36,2,1,""]},"sage.interfaces.scilab.Scilab":{set:[31,1,1,""],console:[31,1,1,""],version:[31,1,1,""],get:[31,1,1,""],whos:[31,1,1,""],sage2scilab_matrix_string:[31,1,1,""],set_seed:[31,1,1,""],eval:[31,1,1,""]},"sage.interfaces.gfan":{Gfan:[14,2,1,""]},"sage.interfaces.mupad.MupadFunction":{trait_names:[42,1,1,""]},"sage.interfaces.expect.Expect":{is_local:[11,1,1,""],user_dir:[11,1,1,""],quit:[11,1,1,""],pid:[11,1,1,""],is_running:[11,1,1,""],is_remote:[11,1,1,""],clear_prompts:[11,1,1,""],expect:[11,1,1,""],eval:[11,1,1,""],interrupt:[11,1,1,""],path:[11,1,1,""],detach:[11,1,1,""]},"sage.interfaces.octave":{octave_console:[32,3,1,""],Octave:[32,2,1,""],octave_version:[32,3,1,""],OctaveElement:[32,2,1,""],reduce_load_Octave:[32,3,1,""]},"sage.interfaces.tachyon.TachyonRT":{"__call__":[6,1,1,""],usage:[6,1,1,""],help:[6,1,1,""]},"sage.interfaces.macaulay2":{macaulay2_console:[25,3,1,""],Macaulay2:[25,2,1,""],remove_output_labels:[25,3,1,""],Macaulay2Element:[25,2,1,""],reduce_load_macaulay2:[25,3,1,""],Macaulay2Function:[25,2,1,""],is_Macaulay2Element:[25,3,1,""]},"sage.interfaces.mupad.Mupad":{set:[42,1,1,""],console:[42,1,1,""],completions:[42,1,1,""],get:[42,1,1,""],cputime:[42,1,1,""],trait_names:[42,1,1,""],expect:[42,1,1,""],eval:[42,1,1,""]},"sage.interfaces.singular":{generate_docstring_dictionary:[41,3,1,""],singular_console:[41,3,1,""],Singular:[41,2,1,""],SingularGBDefaultContext:[41,2,1,""],is_SingularElement:[41,3,1,""],reduce_load_Singular:[41,3,1,""],SingularGBLogPrettyPrinter:[41,2,1,""],SingularError:[41,4,1,""],SingularFunctionElement:[41,2,1,""],singular_gb_standard_options:[41,3,1,""],get_docstring:[41,3,1,""],reduce_load:[41,3,1,""],SingularFunction:[41,2,1,""],SingularElement:[41,2,1,""],singular_version:[41,3,1,""]},"sage.interfaces.rubik.CubexSolver":{format_cube:[36,1,1,""],solve:[36,1,1,""]},"sage.interfaces.qsieve.qsieve_nonblock":{quit:[34,1,1,""],log:[34,1,1,""],pid:[34,1,1,""],list:[34,1,1,""],cputime:[34,1,1,""],n:[34,1,1,""],done:[34,1,1,""],time:[34,1,1,""]},"sage.interfaces.gap":{Gap_generic:[9,2,1,""],is_GapElement:[9,3,1,""],gap_command:[9,3,1,""],gfq_gap_to_sage:[9,3,1,""],reduce_load_GAP:[9,3,1,""],GapFunctionElement:[9,2,1,""],Gap:[9,2,1,""],GapElement_generic:[9,2,1,""],set_gap_memory_pool_size:[9,3,1,""],intmod_gap_to_sage:[9,3,1,""],get_gap_memory_pool_size:[9,3,1,""],gap_console:[9,3,1,""],reduce_load:[9,3,1,""],gap_reset_workspace:[9,3,1,""],GapElement:[9,2,1,""],GapFunction:[9,2,1,""]}},titleterms:{concept:41,help:21,sage:[23,16,26,19],obtain:20,syntax:7,ellipt:17,mwrank:28,paramet:15,involv:1,miscellan:1,readabl:22,siev:34,other:15,matlab:35,factor:[17,7],input:[15,1,41,9,21,7],save:[9,7],axiom:38,real:21,cube:36,"return":15,around:23,read:29,fan:14,kash:21,introduct:41,solver:36,lisp:33,list:21,integ:[21,7],laplac:1,collect:15,integr:21,through:11,tracer:[6,45],vision:45,some:7,continu:1,magma:[15,37],hart:34,todo:[5,22],special:[1,32],variabl:21,definit:7,giac:24,"import":41,complic:7,method:17,matric:1,common:[20,2,11],numer:7,garbag:15,ration:21,free:37,gap3:20,output:1,from:22,qepcad:0,valu:15,polynomi:[21,7],genu:41,tutori:[35,32,1,3,18,7,21,24,41],gener:22,typic:7,assign:[21,7],first:9,load:[9,7],spawn:23,rang:21,pov:45,tachyon:6,number:21,fast:12,chang:[9,20],pitfal:20,quit:8,frobbi:12,pexpect:[1,23,11],interact:1,transform:1,"long":[15,1,41,9,21,7],parallel:26,arithmet:21,interpret:[4,13,26],fraction:1,basic:21,interfac:[0,1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],"function":[21,32,2,7,20,11],macaulay2:25,wrapper:23,tupl:21,imag:22,persist:45,pari:39,gap:9,translat:7,gnu:32,bill:34,calcul:[37,7,39],curv:17,cleaner:16,comput:[12,32,41],"4ti2":30,"abstract":43,indic:13,rai:[6,45],tide:27,file:[29,22],tabl:13,mupad:42,onlin:37,sever:36,quadrat:34,lie:3,octav:32,multipl:15,gnuplot:4,extract:22,mathematica:7,mapl:18,field:21,ideal:12,complex:21,librari:44,rubik:36,groebner:14,singular:[9,41],phc:10,sequenc:21,object:9,monomi:12,data:[29,22],"class":23,latex:1,jmol:22,frica:5,issu:21,which:[9,20],exampl:[15,1,20,9],scilab:31,maxima:[1,43,44]}})12